We study downlink of multiantenna cloud radio access networks (C-RANs) with finite-capacity fronthaul links. The aim is to propose joint designs of beamforming and remote radio head (RRH)-user association, subject to constraints on users' quality-of-service, limited capacity of fronthaul links and transmit power, to maximize the system energy efficiency. To cope with the limited-capacity fronthaul we consider the problem of RRH-user association to select a subset of users that can be served by each RRH. Moreover, different to the conventional power consumption models, we take into account the dependence of baseband signal processing power on the data rate, as well as the dynamics of the efficiency of power amplifiers. The considered problem leads to a mixed binary integer program (MBIP) which is difficult to solve. Our first contribution is to derive a globally optimal solution for the considered problem by customizing a discrete branch-reduce-and-bound (DBRB) approach. Since the global optimization method requires a high computational effort, we further propose two suboptimal solutions able to achieve the near optimal performance but with much reduced complexity. To this end, we transform the design problem into continuous (but inherently nonconvex) programs by two approaches: penalty and \ell_{0}-approximation methods. These resulting continuous nonconvex problems are then solved by the successive convex approximation framework. Numerical results are provided to evaluate the effectiveness of the proposed approaches.