Well over a century ago Charles Darwin redefined biology and introduced the theory of natural selection. One of the problems he encountered was the existence of traits, mainly in males, that seemed to defy the principles of natural selection: they did not aid its bearers in survival and were often outright detrimental. Darwin solved this conundrum by introducing sexual selection. Unlike natural selection where all individuals compete with each other for survival and reproduction, in sexual selection individuals within each sex compete with each other for reproduction. In the original formulation of the principle, Darwin recognized two mechanisms for this. Males would compete with each other for access to females, and females would choose mating partners of their preference. In this opening chapter I want to introduce the topics to be covered in the book, define some basic terms that we will need to understand the subject matter, and define the questions to be asked. My aim for this book is to summarize our growing, yet still comparatively limited empirical knowledge and theory, and to provide suggestions for future research. What interests me most is the relationship between the four forms of sexual selection and their consequences.