\(p\)-compact groups are a homotopy analogue of compact Lie groups. The article presents a survey of the theory of these objects that was developed largely by the author and \textit{C. W. Wilkerson}, e.g. [Ann. Math., II. Ser. 139, No. 2, 395-442 (1994; Zbl 0801.55007)], and by \textit{J. M. Møller} and \textit{D. Notbohm}, e.g. [J. Reine Angew. Math. 456, 99-133 (1994; Zbl 0806.55008)]. The starting point is the fact that a Lie group is (weakly homotopy) equivalent to the loop space of its own classifying space. However, the classifying space is not characterized by this property; therefore, one restricts attention to spaces which are \(\mathbb{F}_p\)-complete (the \(\mathbb{F}_p\)-completion map is an equivalence, \(p\) a prime). A \(p\)-compact group is defined as a space \(X\) having the \(\mathbb{F}_p\)-homology of a finite CW-complex, together with an equivalence with the loop space of an \(\mathbb{F}_p\)-complete space, called \(\text{B} X\). Examples are provided by the \(\mathbb{F}_p\)-completion of compact Lie groups \(G\) such that \(\pi_0G\) is a finite \(p\)-group. The resulting homotopy theory is mostly parallel to that of compact Lie groups.