Beamforming with antenna arrays has been considered as an enabling technology in future wireless communication systems. To conduct beamforming, one has to know the angle-of-departure (AoD) or angle-of-arrival (AoA). For data detection, the receiver also has to know channel response. In this paper, we propose a new joint AoD, AoA, and channel estimation scheme for pilot-assisted multiple-input-multiple-output-orthogonal-frequency-division-multiplexing (MIMO-OFDM) systems. First, a compressive-sensing technique is employed to estimate the channel impulse response, exploiting the sparsity property of wireless channels. Then, AoA and AoD are jointly estimated for each detected path by the maximum likelihood method. The Cramér-Rao lower bound (CRLB) is also derived and a transmit beamforming scheme is proposed accordingly. In the scenario of available prior information, a maximum a posteriori estimation is proposed. The Bayesian CRLB (BCRLB) for the problem is also derived and a transmit beamforming scheme is further proposed. It turns out that only two training OFDM symbols are required for the estimation. Simulation results show that the proposed methods can approach the CRLB/BCRLB in both scenarios and achieve the same spectral efficiency as that obtained with the ideal channel in millimeter-wave communications.