The anima and animus, in Carl Jung's school of analytical psychology, are the two primary anthropomorphic archetypes of the unconscious mind, as opposed to both the theriomorphic and inferior function of the shadow archetypes, as well as the abstract symbol sets that formulate the archetype of the Self. The anima and animus are described by Jung as elements of his theory of the collective unconscious, a domain of the unconscious that transcends the personal psyche. In the unconscious of a man, this archetype finds expression as a feminine inner personality: anima; equivalently, in the unconscious of a woman it is expressed as a masculine inner personality: animus.
The anima and animus can be identified as the totality of the unconscious feminine psychological qualities that a man possesses or the masculine ones possessed by a woman, respectively. It is an archetype of the collective unconscious and not an aggregate of father or mother, brothers, sisters, aunts, uncles, or teachers, though these aspects of the personal unconscious can influence the person for good or ill.
Because a male's sensitivity is often lesser or repressed, the anima is one of the most significant autonomous complexes of all. It is said to manifest itself by appearing in dreams. It also influences a man's interactions with women and his attitudes toward them and vice versa for women and the animus. Jung said that "the encounter with the shadow is the 'apprentice-piece' in the individual's development...that with the anima is the 'masterpiece'". Jung viewed the anima process as being one of the sources of creative ability
Jung believed anima development has four distinct levels, which in "The psychology of the transference" he named Eve, Helen, Mary and Sophia. In broad terms, the entire process of anima development in a man is about the male subject opening up to emotionality , and in that way a broader spirituality, by creating a new conscious paradigm that includes intuitive processes, creativity and imagination, and psychic sensitivity towards himself and others where it might not have existed previously
The first is Eve, named after the Genesis account of Adam and Eve. It deals with the emergence of a man's object of desire.
The second is Helen, an allusion to Helen of Troy in Greek mythology. In this phase, women are viewed as capable of worldly success and of being self-reliant, intelligent and insightful, even if not altogether virtuous. This second phase is meant to show a strong schism in external talents (cultivated business and conventional skills) with lacking internal qualities (inability for virtue, lacking faith or imagination).
The third phase is Mary, named after the Christian theological understanding of the Virgin Mary (Jesus' mother). At this level, women can now seem to possess virtue by the perceiving man (even if in an esoteric and dogmatic way), in as much as certain activities deemed consciously unvirtuous cannot be applied to her
The fourth and final phase of anima development is Sophia, named after the Greek word for wisdom. Complete integration has now occurred, which allows women to be seen and related to as particular individuals who possess both positive and negative qualities. The most important aspect of this final level is that, as the personification "Wisdom" suggests, the anima is now developed enough that no single object can fully and permanently contain the images to which it is related.
Jung focused more on the man's anima and wrote less about the woman's animus. Jung believed that every woman has an analogous animus within her psyche, this being a set of unconscious masculine attributes and potentials. He viewed the animus as being more complex than the anima, postulating that women have a host of animus images whereas the male anima consists only of one dominant image.
Jung stated that there are four parallel levels of animus development in a woman.
1. Man of mere physical power
The animus "first appears as a personification of mere physical power - for instance as an athletic champion or muscle man, such as 'the fictional jungle hero Tarzan'".
2. Man of action or romance
In the next phase, the animus "possesses initiative and the capacity for planned action...the romantic man - the 19th century British poet Byron; or the man of action - America's Ernest Hemingway, war hero, hunter, etc."[
3. Man as a professor, clergyman, orator
In the third; Animus phase, animus becomes the Word ,often appearing as a professor or clergyman....the bearer of the Word - Lloyd George, the great political orator
4. Man as a spiritual guide
"Finally, in his fourth manifestation, the animus is the incarnation of meaning. On this highest level he becomes (like the anima) a mediator of...spiritual profundity". Jung noted that "in mythology, this aspect of the animus appears as Hermes, messenger of the gods; in dreams he is a helpful guide." Like Sophia, this is the highest level of mediation between the unconscious and conscious mind.
The four roles are not identical with genders reversed. Jung believed that while the anima tended to appear as a relatively singular female personality, the animus may consist of a conjunction of multiple male personalities: "in this way the unconscious symbolizes the fact that the animus represents a collective rather than a personal element". 
The process of animus development deals with cultivating an independent and non-socially subjugated idea of self by embodying a deeper word (as per a specific existential outlook) and manifesting this word. To clarify, this does not mean that a female subject becomes more set in her ways (as this word is steeped in emotionality, subjectivity, and a dynamism just as a well-developed anima is) but that she is more internally aware of what she believes and feels, and is more capable of expressing these beliefs and feelings. Thus the "animus in his most developed form sometimes...make[s] her even more receptive than a man to new creative ideas". 
Both final stages of animus and anima development have dynamic qualities (related to the motion and flux of this continual developmental process), open-ended qualities (there is no static perfected ideal or manifestation of the quality in question), and pluralistic qualities (which transcend the need for a singular image, as any subject or object can contain multiple archetypes or even seemingly antithetical roles). They also form bridges to the next archetypal figures to emerge, as "the unconscious again changes its dominant character and appears in a new symbolic form, representing the Self". - the archetypes of the Wise Old Woman/Man
Jungians warned that "every personification of the unconscious - the shadow, the anima, the animus, and the Self - has both a light and a dark aspect....the anima and animus have dual aspects: They can bring life-giving development and creativeness to the personality, or they can cause petrification and physical death".
One danger was of what Jung termed "invasion" of the conscious by the unconscious archetype - "Possession caused by the anima...bad taste: the anima surrounds herself with inferior people". Jung insisted that "a state of anima possession...must be prevented. The anima is thereby forced into the inner world, where she functions as the medium between the ego and the unconscious, as does the persona between the ego and the environment".
Alternatively, over-awareness of the anima or animus could provide a premature conclusion to the individuation process - "a kind of psychological short-circuit, to identify the animus at least provisionally with wholeness". Instead of being "content with an intermediate position", the animus seeks to usurp "the self, with which the patient's animus identifies. This identification is a regular occurrence when the shadow, the dark side, has not been sufficiently realized".
In the book The Invisible Partners it is said that the key to controlling one's anima/animus is to recognize it when it manifests and exercise our ability to discern the anima/animus from reality
“Part of the answer is that self-knowledge has never been one of our strong points. To the contrary, even the most elemental knowledge of oneself is something that most people resist with the greatest determination. Usually it is only when we are in a state of great pain or confusion, and only self-knowledge offers a way out, that we are willing to risk our cherished ideas of what we are like in a confrontation with the truth, and even then many people prefer to live a meaningless life rather than go through the often disagreeable process of coming to know themselves.” -John A.Sanford
"From a reader at goodreads"-Sanford is a Jungian analyst as well as an Episcopalian priest, and he was also a counsellor. This book may not come as easy reading to anyone who isn't open-minded about Jung's findings and analyses, but anyone interested in psychology and human relationships would find this book interesting. I particularly found it interesting how Greek mythology/gods/goddesses/demons are an expression of issues is the realm of the human pysche. I struggled with some of the "darker" parts of the book which explore issues which are totally alien to my understanding, yet overall I found the underlying exploration of the book - that of human love - to be profound, and I particularly enjoyed the closing paragraphs of Chapter 4 where the author examines Christian marriage.
Perhaps it is the anima or animus that leads us to seek out a “Magical Other,” a term coined by Jungian analyst James Hollis to describe “the idea that there is one person out there who is right for us, will make our lives work, a soul–mate who will repair the ravages of our personal history, one who will be there for us, will read our minds, know what we want and meet those deepest needs; a good parent who will protect us from suffering and spare us the challenging journey of individuation.”2 Such romantic fantasies may drive us to search endlessly for our “perfect” match, or fixate in fascinated longing for an Other who seems to be our “ideal.”
So love for an Other can serve as a fire that lights the way on our own journey, helping us to better understand ourselves. Even disappointments in relationship may hold an opportunity for personal development. I remember an afternoon I spent sitting with a loved one and telling her about an experience of heartbreak. After listening to my story, she asked what attracted me to the person I’d been discussing. When I told her, she replied, “He’s a mirror.”
Therefore, we can use those characteristics we admire in the Other as a guide for our own evolution, and work on developing our own inner opposite, rather than searching for someone else to “complete” us. “Consider the courage of those truly willing to look within and own what they find,”2 Hollis says. In doing so, we can make the effects of the anima and animus conscious, possibly helping us discover our own gifts and purpose in the process.
Additionally, one of the tasks of individuation is to integrate the anima or animus in an internal marriage of the masculine and feminine parts of the psyche. Hollis writes, “Hierosgamos, the sacred marriage, properly honors the other as Other and at the same time protects the absolute uniqueness of the individual partners.”2 Through such inner work, we become free to truly love the Other as they are, rather than our projections or fantasies of them. Or as Alan Watts said, “When you’re loving somebody, you are simply delighting in that person as such.”