Task semantics can be expressed by a set of input-output examples or a piece of textual instruction. Conventional machine learning approaches for natural language processing (NLP) mainly rely on the availability of large-scale sets of task-specific examples. Two issues arise: first, collecting task-specific labeled examples does not apply to scenarios where tasks may be too complicated or costly to annotate, or the system is required to handle a new task immediately; second, this is not user-friendly since end-users are probably more willing to provide task description rather than a set of examples before using the system. Therefore, the community is paying increasing interest in a new supervision-seeking paradigm for NLP: learning to follow task instructions, i.e., instruction following. Despite its impressive progress, there are some common issues that the community struggles with. This survey paper tries to summarize and provide insights to the current research on instruction following, particularly, by answering the following questions: (i) What is task instruction, and what instruction types exist? (ii) How to model instructions? (iii) What are popular instruction following datasets and evaluation metrics? (iv) What factors influence and explain the instructions' performance? (v) What challenges remain in instruction following? To our knowledge, this is the first comprehensive survey about instruction following.