The theory of electron transport via hopping between localised states is developed within the framework of the rate equation approach and in particular the a.c and d.c. conductivity and Hall mobility are considered. The existence of substantial experimental data on the a.c. and d.c. conductivities motivates the development of a unified theory for these quantities. The availability of exact asymptotic conductivity formulae and computer generated data for a variety of special cases enables the validation of any particular approximation scheme prior to the analysis of experimental data. This in turn enables an unambiguous evaluation of the rate equation approach as a quantitative theory of transport in real systems. The conductivity problem has two congruent representations; either a single particle random walk on a random lattice or an equivalent electrical circuit may be considered. In this work we examine both approaches and compare and contrast the methods used. Previous unified theories were exclusively based on the random walk approach and methods for evaluating the associated average Breen’s function; these methods are critically reviewed and extended. The equivalent circuit approach is then examined and a new theory is formulated which is simple to develop and yields improved results which agree well with asymptotic formulae and computer simulation data. Experimental data on a variety of systems is analysed; the extent of agreement obtained depends on the type of system considered and in some situations good agreement is found. Various problems are isolated which relate to the application of the rate equation model rather than the approximations used. Finally the hopping Hall effect is considered. The lack of any reliable experimental data reduces the interest in the phenomenological aspect of the problem. However there exists computer simulation data; the utility and simplicity of the equivalent circuit approach is further demonstrated by the derivation of a theory that agrees with this data.