Studying the properties of individual events and molecules offers a host of advantages over taking only macroscopic measurements of populations. Here we review such advantages, as well as some pitfalls, focusing on examples from biological imaging. Examples include single proteins, their interactions in cells, organelles, and their interactions both with each other and with parts of the cell. Additionally, we discuss constraints that limit the study of single events, along with the criteria that must be fulfilled to determine whether single molecules or events are being detected.