Over the past five years, deep learning techniques have led to astounding breakthroughs in many areas, like speech recognition and computer vision applications. The application of deep learning in the radar domain has however been rather limited. The merit of using deep learning techniques for the purpose of human gait classification in radar is investigated. Several models based on three deep neural network architectures, the multi-layer perceptron, the autoencoder and the convolutional neural network, are used to distinguish human walking and running gaits from non-gait signatures in radar micro-Doppler spectrograms. The effects of model architecture, size and depth are analyzed and convolutional models are proven to be the most effective. A deep convolutional neural network (DCNN) is designed to distinguish the number of human gaits in a multi-target classification scenario. Experimental data includes synthetic data at several radar frequencies and SNR levels, as well as X-band CW radar measurements taken at various ranges. The effects on the performance of the DCNN are investigated by varying with regularization methods, the amount of training data, training algorithms, parameter initialization, and transfer learning. Deep learning techniques, and convolutional neural networks in particular, are proven to be an effective approach for human gait classification in radar.