This chapter is devoted to time-dependent quantum electronic transport in a multi-terminal junction when the applied biases generally depend on time, e.g. a switch-on problem. Our consideration here is based on the partition-free approach in which, prior to the biases being switched on, the whole system was fully interacting and equilibrated. A general case of the tight-binding Hamiltonian is studied in great detail within the wide-band approximation, when exact analytical solutions for the NEGF and the current are possible. This is followed by a general discussion of the double time propagation method, which is valid for a general case of non-zero interactions within the central region. Then we consider the method of Croy and Salmann, which goes beyond the wide-band approximation, and the finite system method due to Perfetto, Stefanucci and Cini. Finally, we discuss quantum noise and, in that context, consider the current–current correlation function in the general time-dependent setting, derive a general formula for it and consider the problem of the traverse junction time using a graphene nanoribbon as an example.