Sexual selection is responsible for a great diversity of elaborate male traits. A general female preference for males that have exaggerated traits drives this process, but the reasons females exhibit this preference are often unclear. Recent advances in understanding signal evolution have emerged from studies of receiver psychology that focus on how receivers perceive and process communication signals. I apply the perspective of receiver psychology to understand female preference for elaborate signals in túngara frogs (Physalaemus pustulosus). Male túngara frogs produce advertisement calls of variable complexity. Females exhibit a strong preference for complex to simple calls, but previous studies have not found consistent patterns of preference between calls of variable complexity. In my doctoral research, I investigate the function of variable complexity in túngara frogs. Specifically, I address the following questions: 1) Are calls of variable complexity especially relevant to females in certain contexts? Do males respond to female behavior by increasing their production of complex calls? 2) Does male to female proximity influence female response to call complexity? 3) Are females constrained by their perceptual biology in discriminating differences in call complexity? 4) Can females remember attractive males over silences between bouts of advertising? Is working memory for attractive males dependent upon signal complexity? And 5) Does signal memorability increase with signal complexity in a linear relationship? These studies provide several new perspectives to an understanding of female preference for elaborate signals. Phonotaxis experiments demonstrate that females use elicitation behaviors to influence male production of complex calls, that proximity influences female response to signal elaboration, that females are constrained by their perceptual biology in discriminating between complex calls, that memory can influence the evolution of signal complexity, and that memorability and signal complexity share a non-linear relationship. / text