This study investigates deep learning based single- and multi-channel speech dereverberation. For single-channel processing, we extend magnitude-domain masking and mapping based dereverberation to complex-domain mapping, where deep neural networks (DNNs) are trained to predict the real and imaginary (RI) components of the direct-path signal from reverberant (and noisy) ones. For multi-channel processing, we first compute a minimum variance distortionless response (MVDR) beamformer to cancel the direct-path signal, and then feed the RI components of the cancelled signal, which is expected to be a filtered version of non-target signals, as additional features to perform dereverberation. Trained on a large dataset of simulated room impulse responses, our models show excellent speech dereverberation and recognition performance on the test set of the REVERB challenge, consistently better than single- and multi-channel weighted prediction error (WPE) algorithms.