Kaleidoscopes are optical instruments for creating and observing visually attractive patterns. Two mathematical concepts that are closely related to kaleidoscopes are symmetries and groups, so they determine two main chapters of this paper. Depending on the number of mirrors inside the kaleidoscope, and the dimension of the space we observe it in, kaleidoscope can form two-dimensional, three-dimensional or abstract multidimensional patterns. This paper is focused on two-dimensional and three-dimensional patterns and their symmetries. Our goal is the determination of the symmetries of a pattern based on type of kaleidoscope that formed it, and also the determination of the type of kaleidoscope based on symmetries of the resulting pattern. Symmetries of patterns created by kaleidoscopes, together with the operation of composition, form a group. Next, we give an overview of known symmetry groups related to two-dimensional and three-dimensional patterns: rosette groups, wallpaper groups, three dimensional point groups and space groups. Two-dimensional kaleidoscopes with two mirrors generate rosette groups. Two-dimensional kaleidoscopes with three and four mirrors generate certain wallpaper groups. Three-dimensional kaleidoscopes with three mirrors generate certain three-dimensional point groups. ”Closed box” kaleidoscopes generate certain space groups.