A useful, although reductive, theory on attraction comes from evolutionary psychology. It holds that we are drawn to others on the basis of our assessment of their reproductive fitness. We weigh up physical qualities (symmetry, health, youth, strength in men, child-bearing indicators in women), material possessions (wealth), social skills (status, charity, humour, confidence) and cultural factors (fashion, weight, skin tone, hair styles, body decoration). We have roughly standardized perceptions of 'attractive' individuals, though it can vary over history and in different parts of the world.
Generally speaking, we select partners that are roughly similar to our own level of 'reproductive attractiveness' (measured in the wide sense). This means that it is not only the most 'attractive' individuals who manage to form partnershipsthere is someone for everyone.
An excellent book that deals with attraction from an evolutionary perspective is 'The Mating Mind: How Sexual Choice Shaped the Evolution of Human Nature' by Geoffrey Miller. His hypothesis is that a lot of how we conduct our lives e.g. high status jobs, creative work, being charitable or popular for example, sends signals to attract potential partners.
Ideas about compatibility include 'opposites attract' and 'like-minded attract'. There seems to be clinical support for both positions. On the one hand we may be drawn to individuals who have characteristics we lack. They may reflect our shadow side - the elements that reside within us but which we refuse to acknowledge. They may also balance or complement our personalities. Some examples of differences include highly-driven v. relaxed, artistic v. scientific, sporty v. sedate and introverted v. extroverted. On the other hand, like-minded individuals may connect well because it widens the field of interaction, for example sports lovers can play and watch games together, and extroverts can socialize happily. What seems important in either of these positions is that the underlying core values are congruent. Ethical and social ideals tend to be matched in solid partnerships.
Various factors can be at play during the initial attraction. Sometimes it begins as physical impulsepheromones doing their workand sometimes it starts as an emotional connection first. Usually it involves an implicit assessment of the other's suitability as a potential mate (genetic donor) and/or a long-term partner (protector of self and of future offspring). This entails a complex interplay of observation (often matching them up to our ideal, or even setting them up as an ideal), reaction (via chemicals and body language) and interaction.
An available person is likely to send out the right signals when they are self-contented. It is a clich', but a relevant one - when we can accept and love ourselves, we are in a good position to be accepted and loved by another. Inner confidence makes itself visible to potential partners. It is more convincing than 'fake' confidence (though sometimes in imagining ourselves confident, we can become it). This is why many happily committed individuals can be so appealing to others.
There are more and more forums for finding love including internet, speed-dating, lonely-hearts columns and match-making services. There have been many success stories linked with these platforms and they are drawing a wide audience. They are effective in part because they exclude individuals who are not looking for romance. The drawbacks can be that we don't have time to see the individual in roles other than as a 'potential date'. Also, increasingly relationships begin in the virtual sphere (online, SMS texts) which can remove some of the depth of a real relationship including the pain of being rejected. For clients in therapy who are considering more traditional meeting grounds, we explore options such as taking up hobbies, playing sports, joining clubs or organizing friendly dinner parties (perhaps asking friends to bring a single friend). These activities are rewarding in their own right, and carry the bonus of forming friendships and partnerships.