Semantic Matching in Search is a systematic and detailed introduction to newly developed machine learning technologies for query document matching (semantic matching) in search, particularly in web search. It focuses on the fundamental problems, as well as the state-of-the-art solutions of query document matching on form aspect, phrase aspect, word sense aspect, topic aspect, and structure aspect. Matching between query and document is not limited to search, and similar problems can be found in question answering, online advertising, cross-language information retrieval, machine translation, recommender systems, link prediction, image annotation, drug design, and other applications where one is faced with the general task of matching between objects from two different spaces. The technologies introduced in this monograph can be generalized into more general machine learning techniques, which are referred to as learning to match in this survey. It is hoped that the ideas and solutions explained in Semantic Matching in Search may motivate industrial practitioners to turn the research results into products. The methods introduced and the discussions around them should also stimulate academic researchers to find new research directions and approaches.