Let a reductive group G act on a scheme X. If L is a line bundle over X, a linearisation of L will correspond to a lifting of the action on G to a bundle action of G on L. I will provide a few examples, discuss why this is an important concept in Geometric Invariant Theory, and then present a few results in the general thoery of G-linearisations. In particular, I shall present some facts on uniqueness of linearisations, and show that for normal varieties over algebraically closed fields, one can always find an integer such that the line bundle L^n is linearisable.