Given a graph X and a group G we may construct a covering graph Cov(X,Z) by means of a function (called a voltage assignment) Z, that maps arcs of the graph X to elements of the group G. The graph Cov(X,Z) is called the regular cover of X arising from the voltage graph (X,Z) and admits a semiregular (fixed point free) group of automorphisms isomorphic to G. Every graph X with a semiregular group of automorphism G can be regarded as the regular cover of the quotient graph X/G with an appropriate voltage assignment. The theory of voltage graphs and their associated regular covers has become an important tool in the study of symmetries of graphs. We present a generalised theory of voltage graphs where G is allowed to be an arbitrary group (not necesarilly semiregular).