Associated to every smooth curve one can associate a compact group called its Jacobian. Classically, the concept was introduced by Riemann and has roots in the work of Bernoulli, Euler, Abel, Jacobi, and Legendre. A nodal curve may be thought of as a limit of smooth curves. I will discuss (generalized) Jacobians associated to such curves. In this setting, the combinatorics of the "dual graph" play an essential role. I will describe how one can compute some very general invariants for these objects in terms of the combinatorics of the dual graph. This talk is based on joint work with Alberto Bellardini.