In this talk we consider a conservation law (or a system of conservation laws) on a network consisting in a finite number of arcs and vertices. This setting is justified by various applications, such as car traffic, gas pipelines, data networks, supply chains, blood circulation and so on. The key point in the extension of conservation laws on networks is to define solutions at vertices. Indeed, it is sufficient to define solutions only for Riemann problems at vertices, i.e. Cauchy problems with constant initial data in each arc of the junction. We present some different possibilities to produce solutions to Riemann problems at vertices. Moreover we consider the general Cauchy problem on the network. We explain how to prove existence of a solution both in the scalar case and in the case of systems. In particular, for the scalar case, we introduce general properties on Riemann solvers at vertices, which permit to have existence of solutions for the Cauchy problem.