The vocabulary mismatch problem is a long-standing problem in information retrieval. Semantic matching holds the promise of solving the problem. Recent advances in language technology have given rise to unsupervised neural models for learning representations of words as well as bigger textual units. Such representations enable powerful semantic matching methods. This survey is meant as an introduction to the use of neural models for semantic matching. To remain focused we limit ourselves to web search. We detail the required background and terminology, a taxonomy grouping the rapidly growing body of work in the area, and then survey work on neural models for semantic matching in the context of three tasks: query suggestion, ad retrieval, and document retrieval. We include a section on resources and best practices that we believe will help readers who are new to the area. We conclude with an assessment of the state-of-the-art and suggestions for future work.