A polymer brush can be defined as a dense array of polymers end-attached to an interface that stretch out into the surrounding medium. Polymer brushes have been investigated for the past 30 years and have shown to be an extremely useful tool to control interfacial properties. This review is intended as an introduction into this very vibrant and diverse topic. We start by giving a clear definition of the polymer brush and we discuss its structure and properties. Next, we give an overview of the wide array of applications of polymer brushes, such as its use to prevent fouling, to stabilize particle suspensions and to reduce friction. We continue by giving an overview of the typical methods to produce polymer brushes, and end by reviewing recent work on the topic of responsive polymer brushes and discussing possible directions for future research.