Often in political parlance the phrase "the market" is used quite broadly to cover a wide variety of voluntary economic institutions, including firms, non-profit organizations, families, and so on in addition to markets proper. But traditional neoclassical economics is about ideal markets proper: instantaneous buying and selling on a costless spot exchange. Ronald Coase started expanding the scope of economics with his work on the firm, and this line of thinking has developed into a school, often called the "new institutional economics" or NIE that focuses on non-market or partial-market voluntary economic institutions as well as on the conditions that must be satisfied for efficient markets to be possible. The economics Nobel committee has finally recognized the study of non-market but voluntary economic institutions with its awards this year to Oliver Williamson and Elinor Ostrom.
Williamson and his fellow travelers Oliver Hart, Yoram Barzel, Steven Cheung, and Janet Landa have long influenced my thinking about measuring value, mental transaction costs, smart contracts,
the origins of money, and more.
The new institutional economics school in a nutshell holds that often transaction costs are too high for spot markets to work properly. If spot markets were perfectly efficient we would not need firms or long-term contracts, for example, but in fact we have those and many other institutions besides pure markets. The NIE studies and has started to explain the functions of institutions that are not markets proper, such as long-term contracts and firms, as well as the legal underpinnings of market economies, especially property and contracts. Contracts and property are the main formal expressions of economic relations recognized by the NIE, which makes this school especially interesting to someone like me interested in the economic role of contracts and property and how to adapt these institutions to (and even to some extent incorporate them into) evolving technology.
Note that these institutions are "voluntary" in the sense of the traditional common-law principle of non-initiation of force, and assume a sophisticated legal framework. When this assumption doesn't hold, these principles usually work in a very different way or don't work at all, and one has to be very careful applying them. (See here and here for more on the problem of coercive externalities).
Meanwhile, here is a good article introducing the other economics Nobel winner this year, Elinor Ostrom.