In this thesis we study plane-wave limits and M-theory vacua. We consider several hereditary properties of the plane-wave limit but focus on that of homogeneity. We show that a sufficient condition for a plane-wave limit along a particular geodesic of any spacetime to be homogeneous is that the geodesic be homogeneous. On reductive homogeneous spacetimes we reduce the calculation to a set of algebraic formulae by two different methods; the first uses the covariant description of the plane-wave limit [Blau, O’Loughlin, Papadopoulos. JHEP,01:047,2002] and the second employs a non-adapted coordinate description of the plane-wave limit. We study how the homogeneous structure on a reductive homogeneous spacetime behaves under the plane-wave limit and apply our formulae to many relevant examples. We then consider supersymmetric M-theory vacua and the Lie supersymmetry superalgebra on these backgrounds. We show that those backgrounds which preserve more than 24 of the supersymmetries are necessarily homogeneous and provide some evidence that this boundary is sharp. The symmetric square of the spinor bundle of an 11-dimensional spacetime is isomorphic to a particular bundle of differential forms, this can be used to interpret Killing spinors as differential forms satisfying a system of first order equations [Gauntlett, Gutowski, Pakis. JHEP,12:049,2003]. We use this technique to investigate both the geometric and algebraic nature of the 24+ supergravity solutions, in particular those which are plane-waves. Finally we consider some more general homogeneous supergravity solutions, including homogeneous 5-dimensional supergravity.