  We give a survey of the representation theory of $\mathrm{GL}_N$ over finite
local principal ideal rings via Clifford theory, with an emphasis on the
construction of regular representations. We review results of Shintani and
Hill, and the generalisation of Takase. We then summarise the main features,
with some details but without proofs, of the recent constructions of regular
representations due to Krakovski--Onn--Singla and Stasinski--Stevens,
respectively.
