Spiral similarity is the mapping of the Euclidean plane given as a composition of homothety and rotation with a common center. This paper presents the basic theorems on spiral similarity and some of its applications in solving complex problems in the field of planimetry. The introductory chapter gives an overview of the known similarity mappings and highlights the place of the spiral similarity among them. It is noticed that it is useful to present the spiral similarity as a geometric interpretation of the product of two complex numbers, and the existence and uniqueness of the spiral similarity is proven, which for a given pair of line segments maps one onto another. Further theorems describe the determination of the center of spiral similarity in different cases and it is observed that spiral similarities always occur in pairs. The notion of a symmedian in a triangle is defined and its connection with the position of the center of the spiral similarity is explained. In order to solve problems in which spiral similarity is applied, some other concepts and results are set forth, mainly related to the geometry of a circle, such as the Apollonius circle, inversion and Pascal’s theorem. The final and the most comprehensive chapter consists of solutions to several problems from the International Mathematical Olympiad (IMO) and from mathematical competitions in Japan, South Korea and Iran. In each solution, spiral similarity is applied. This approach is not always the most practical one, but the examples are suitable for observing the role of spiral similarity.