Deep neural networks have achieved near-human accuracy levels in various types of classification and prediction tasks including images, text, speech, and video data. However, the networks continue to be treated mostly as black-box function approximators, mapping a given input to a classification output. The next step in this human-machine evolutionary process-incorporating these networks into mission critical processes such as medical diagnosis, planning and control-requires a level of trust association with the machine output. Typically, statistical metrics are used to quantify the uncertainty of an output. However, the notion of trust also depends on the visibility that a human has into the working of the machine. In other words, the neural network should provide human-understandable justifications for its output leading to insights about the inner workings. We call such models as interpretable deep networks. Interpretability is not a monolithic notion. In fact, the subjectivity of an interpretation, due to different levels of human understanding, implies that there must be a multitude of dimensions that together constitute interpretability. In addition, the interpretation itself can be provided either in terms of the low-level network parameters, or in terms of input features used by the model. In this paper, we outline some of the dimensions that are useful for model interpretability, and categorize prior work along those dimensions. In the process, we perform a gap analysis of what needs to be done to improve model interpretability.