Unitary fusion categories are a class of rich algebraic objects, with deep connections to many areas of mathematics and physics. One of the simplest examples of a unitary fusion category is the representation category of a finite group. I will discuss this example in detail, explaining the structure it possesses to make it a unitary fusion category. Inspired the classification of finite simple groups, research on unitary fusion categories focusses on providing classification results. In this talk I will discuss several of these classifications, including the main result of my thesis, the classification of unitary fusion categories generated by a normal object of dimension less than 2.