In article reveals, proceeding from the modern paradigm of sociology of a family and the institutional theory, a family entity as social institute and as small social group; classification of families both in a retrospective, and in the current social situation is given; in a debatable key functions of the modern family are singled out, reveal and added; the general and specific political, economic social and other background in which function is shown and functions of a family are implemented now (including in Russia); for the first time in family sociology, in a semyevedeniye the hypothesis of existence and implementation of dysfunctionality of a family is made; at the same time are delimited and justified dysfunctionality of a family of four types having the conditions, the reasons, factors and levels of a materialization; proceeding from explained, conceptual sentences on «smoothing» / elimination of dysfunctionality of a family are defined and reasoned; positive results of this process are explained.