Psychology and neuroscience are concerned with the study of behavior, of internal cognitive processes, and their neural foundations. However, most laboratory studies use constrained experimental settings that greatly limit the range of behaviors that can be expressed. While focusing on restricted settings ensures methodological control, it risks impoverishing the object of study: by restricting behavior, we might miss key aspects of cognitive and neural function. In this article, we argue that psychology and neuroscience should increasingly adopt innovative experimental designs, measurement methods, analysis techniques and sophisticated computational models to probe rich, ecologically valid forms of behavior, including social behavior. We discuss the challenges of studying rich forms of behavior as well as the novel opportunities offered by state-of-the-art methodologies and new sensing technologies, and we highlight the importance of developing sophisticated formal models. We exemplify our arguments by reviewing some recent streams of research in psychology, neuroscience and other fields (e.g., sports analytics, ethology and robotics) that have addressed rich forms of behavior in a model-based manner. We hope that these "success cases" will encourage psychologists and neuroscientists to extend their toolbox of techniques with sophisticated behavioral models – and to use them to study rich forms of behavior as well as the cognitive and neural processes that they engage.