With the advent of deep learning, a lot of progress has been made towards algorithm development to solve a plethora of practical problems in Natural Language Processing. These algorithms incorporate highly complex networks, which are becoming increasingly difficult to explain theoretically. The difficulty is exacerbated even further due to the recent trends of extremely large networks which are trained on datasets of size in the order of billions (for example, GPT-3). It has been seen that models often pick up a lot of human biases and spurious patterns from the data and can also lead to offensive results (like Microsoft Tay, or Amazon's Recruiting tool). Thus, it has become necessary to understand the working of these networks to establish trust and ensure fairness and safety before there are deployable in large production environments. Also, this understanding can help unravel shortcomings which can lead to better algorithm development. In recent years, various approaches have been proposed to explain model predictions in a network-agnostic way or with limited assumptions about the network. This talk will focus on these approaches in the context of NLP, starting with motivating applications, touching upon the basic paradigms of explainability, following up with discussion on influential approaches, and laying the ground for research gaps and current trends.