The multidisciplinary field of personal relationships has focused primarily on strong ties (romantic relationships, friendships, family relationships). However, acquaintances (weak ties) are pervasive in people's lives, contribute to well‐being, influence strong ties, and can become strong ties over time. This review article synthesizes several areas of literature about the role of acquaintances (weak ties) in the web of relationships and about the formation of acquaintanceships. The terms acquaintances and weak ties are used interchangeably in this article to refer to the type of relationship that exists in the peripheral layers of social networks. In the first section, I discuss the literature on factors associated with the size of people's acquaintance network, needs met by acquaintances (compared to those of closer ties), health and happiness benefits of interaction with acquaintances, and the dark side of acquaintances including having unwanted acquaintances. In the second section, I discuss how acquaintanceships are formed, and particularly the type that can develop into a closer tie. This section summarizes research from the literatures on friendship formation, relationship initiation, attraction, and first interactions of dyads at zero‐acquaintance. I end the article by identifying several research topics on acquaintances that could be studied by the next generation of scholars.