In my talk, I aim to give an accessible overview of my PhD research, where I studied smooth complex representations of covers of reductive p-adic groups. An example of such a covering group is the metaplectic group, which is a double cover of the symplectic group. The metaplectic group fits into a more general framework developed by Brylinski and Deligne. The first part of my talk gives an introduction to (Brylinksi-Deligne) covers of reductive p-adic groups, with some examples. After that, I will move on to the representation theory. The main result of my PhD research is a formula for the Harish-Chandra mu-function for covering groups, which is defined using intertwining operators between parabolically induced representations. This result generalizes Silberger's formula for reductive groups, however the proof is different. I will present this result, together with the necessary context and motivation. If time allows it, I will discuss additional results and further directions.