DNA is probably the molecule that carries the highest possible density of information. Information comes along with structuring and recognition that offer the possibility of using DNA to build self-assembled molecular circuits for nanoelectronics applications. This, however, must be complemented by suitable conductivity, which was tested in a series of experiments on charge migration along DNA molecules. These issues together with reports on possible high rates of charge transfer between donor and acceptor through the DNA, obtained in the last decade from solution chemistry experiments on large numbers of molecules, triggered a series of direct electrical transport measurements through DNA single molecules, bundles and networks. These measurements are reviewed and presented here. From these experiments we conclude that electrical transport is feasible in short DNA molecules, in bundles and networks, but blocked in long single molecules that are attached to surfaces.