I did a deep dive on this a few weeks ago. If you're interested, the following is what I what I think were the most interesting studies. Sorry for my personal citation style. My conclusion is that there are differences, some of them not as big as claimed in popular media and for the majority we don't know their origin.
Buss. 1989. Sex differences in human mate preferences: Evolutionary hypotheses tested in 37 cultures
Feingold. 1994. Gender Differences in Personality: A Meta-Analysis
Grijalva et al. 2014. Gender Differences in Narcissism: A Meta-Analytic Review
Hall, Canterberry. 2011. Sexism and Assertive Courtship Strategies
Joseph, Newman. 2010. Emotional Intelligence: An Integrative Meta-Analysis and Cascading Model
Lukaszewski, Roney. 2010. Kind toward whom? Mate preferences for personality traits are target specific
Oliver, Hyde. 1993. Gender Differences in Sexuality: A Meta-analysis
Snyder et al. 2008. The dominance dilemma: Do women really prefer dominant mates?
Su, Rounds, Armstrong. 2009. Men and Things, Women and People
Wood, Eagly. 2002. A Cross-Cultural Analysis of the Behavior of Women and Men: Implications for the Origins of Sex Differences
Buss. 1989. Sex differences in human mate preferences: Evolutionary hypotheses tested in 37 cultures
Feingold. 1994. Gender Differences in Personality: A Meta-Analysis
Grijalva et al. 2014. Gender Differences in Narcissism: A Meta-Analytic Review
Hall, Canterberry. 2011. Sexism and Assertive Courtship Strategies
Joseph, Newman. 2010. Emotional Intelligence: An Integrative Meta-Analysis and Cascading Model
Lukaszewski, Roney. 2010. Kind toward whom? Mate preferences for personality traits are target specific
Oliver, Hyde. 1993. Gender Differences in Sexuality: A Meta-analysis
Snyder et al. 2008. The dominance dilemma: Do women really prefer dominant mates?
Su, Rounds, Armstrong. 2009. Men and Things, Women and People
Wood, Eagly. 2002. A Cross-Cultural Analysis of the Behavior of Women and Men: Implications for the Origins of Sex Differences