This paper develops a new equilibrium model of two-sided search where ex-ante heterogenous individuals have general payoff functions and vectors of attributes. The analysis applies to a large class of models, from the non-transferable utility case to the collective household case with bargaining. The approach is powerful for it identifies a simple algorithm which, in the empirical application, is found to rapidly converge to equilibrium. Using indirect inference, we identify the differential effects of women's ability and charm on female match incentives. We use these results to assess the separate impacts of the arrival of equal opportunities for women in the labor market and the advent of the contraceptive pill on female economic activity and matching.