How does the brain represent different modes of information? Can we design a system that automatically understands what the user is thinking? Such questions can be answered by studying brain recordings like functional magnetic resonance imaging (fMRI). As a first step, the neuroscience community has contributed several large cognitive neuroscience datasets related to passive reading/listening/viewing of concept words, narratives, pictures and movies. Encoding and decoding models using these datasets have also been proposed in the past two decades. These models serve as additional tools for basic research in cognitive science and neuroscience. Encoding models aim at generating fMRI brain representations given a stimulus automatically. They have several practical applications in evaluating and diagnosing neurological conditions and thus also help design therapies for brain damage. Decoding models solve the inverse problem of reconstructing the stimuli given the fMRI. They are useful for designing brain-machine or brain-computer interfaces. Inspired by the effectiveness of deep learning models for natural language processing, computer vision, and speech, recently several neural encoding and decoding models have been proposed. In this survey, we will first discuss popular representations of language, vision and speech stimuli, and present a summary of neuroscience datasets. Further, we will review popular deep learning based encoding and decoding architectures and note their benefits and limitations. Finally, we will conclude with a brief summary and discussion about future trends.