This Dissertation concerns phases of matter with various ``subdimensional'' properties. We start with topologically ordered phases with subdimensional properties. This includes a discussion of fracton topologically ordered phases, resonating valence plaquette phases, and floating topological phases. We then move on to discuss systems with symmetries that act on subdimensional subsystems, in particular those with line-like subsystems in 2D or planar subsystems in 3D. A classification of symmetry-protected topological (SPT) phases protected by such symmetries is presented. Finally, we discuss symmetries which act on fractal dimensional subsystems and a classification of such phases.