Summary: We study spherically symmetric solutions to the Einstein field equations under the assumption that the space-time may possess an arbitrary number of spatial dimensions. The general solution of Synge is extended to describe systems of any dimension. Analogues of four-dimensional solutions for arbitrary dimension are also presented, derived using the above scheme. Finally, we discuss the requirements for the existence of Birkhoff’s theorems in space-times of arbitrary dimension with or without matter fields present. Cases are discussed in which the assumptions of the theorem are considerably weakened yet the theorem still holds. We also discuss the situations in which the weakening of certain conditions may cause the theorem to fail.