(2+1)-dimensional topological phases of matter (TPM) promise a route to quantum computation where quantum information is topologically protected against decoherence. In this talk, we will explore the underling mathematical theory that is driving the classification of these TPM. We will mainly concentrate on the algebraic/categorical structure behind such phases and explain where this structure fits in describing TPM. Finally, we will discuss some recent developments in the mathematical classification pertinent to TPM.