  Monogamy is an intrinsic feature of quantum correlations that gives rise to
several interesting quantum characteristics which are not amenable to classical
explanations. The monogamy property imposes physical restrictions on
unconditional sharability of quantum correlations between the different parts
of a multipartite quantum system, and thus has a direct bearing on the
cooperative properties of states of multiparty systems, including large
many-body systems. On the contrary, a certain party can be maximally classical
correlated with an arbitrary number of parties in a multiparty system. In
recent years, the monogamy property of quantum correlations has been applied to
understand several key aspects of quantum physics, including distribution of
quantum resources, security in quantum communication, critical phenomena, and
quantum biology. In this chapter, we look at some of the salient developments
and applications in quantum physics that have been closely associated with the
monogamy of quantum discord, and "discord-like" quantum correlation measures.
