In this paper, we consider the (global and sum) energy efficiency optimization problem in downlink multi-input multi-output multi-cell systems, where all users suffer from multi-user interference. This is a challenging problem due to several reasons: First, it is a nonconvex fractional programming problem; second, the transmission rate functions are characterized by (complex-valued) transmit covariance matrices; and third the processing-related power consumption may depend on the transmission rate. We tackle this problem by the successive pseudoconvex approximation approach, and we argue that pseudoconvex optimization plays a fundamental role in designing novel iterative algorithms, not only because every locally optimal point of a pseudoconvex optimization problem is also globally optimal but also because a descent direction is easily obtained from every optimal point of a pseudoconvex optimization problem. The proposed algorithms have the following advantages: First, fast convergence as the structure of the original optimization problem is preserved as much as possible in the approximate problem solved in each iteration; second, easy implementation as each approximate problem is suitable for parallel computation and its solution has a closed-form expression; and third, guaranteed convergence to a stationary point or a Karush-Kuhn-Tucker point. The advantages of the proposed algorithm are also illustrated numerically.