The author studies representations of Lie colour algebras \(\mathfrak g\) and restricted Lie colour algebras \(\mathfrak g\), usually related to properties of \(\mathfrak g\) and of its (restricted) universal enveloping algebra. The grading is by a commutative group \(\Gamma\) with an additive form \(( ,)\) of \(\Gamma\times \Gamma\) into the invertible elements of the commutative base ring such that \((\alpha,\beta) = (\beta,\alpha)^{-1}\) for \(\alpha,\beta\) in \(\Gamma\). A key role is played by complete sets of modules, i.e. families of (restricted) \(\mathfrak g\)-modules for which the intersection of the annihilators of the modules in the family is zero. When the modules are finite-dimensional, this relates to residually finite properties of \(\mathfrak g\). A theorem of Burnside is generalized to restricted Lie colour algebras, and applications are given to the blocks of supersolvable restricted Lie colour algebras. There is also an application which characterizes \(p\)-reductive restricted Lie colour algebras in several ways, and also characterizes finite-dimensional restricted Lie colour algebras whose semisimple restricted modules are closed under tensor products. Some (unrestricted) results concern strictly triangulable modules and the nilpotency of \(\mathfrak g\). Some other restricted results concern various radicals of \(\mathfrak g\), the nilpotency of \(\mathfrak g\), and the case when \(\mathfrak g\) is a torus.