The so-called (2,0) superconformal field theory (SCFT) in six dimensions has been at the epicentre of attention in formal high-energy theory for two decades. Despite its fundamental importance (it is believed to capture the low-energy dynamics of multiple M5-branes in M-theory and also is a very special SCFT in its own right) many of its aspects still remain mysterious; for example it has no known Lagrangian description. The aim of this project is to take advantage of recent progress in exact Quantum Field Theory methods, such as supersymmetric localisation and the superconformal index, in order to better understand the relationship between the (2,0) SCFT and lower-dimensional (4D,5D) theories related to it via compactification. In the process, aspects of the lower-dimensional theories will also be investigated.