Chemical cells that spontaneously form in simple inorganic systems are presented. The cells are surrounded by semipermeable membranes that allow water and some ions to diffuse through. These cells exhibit dynamical behaviors that are typically associated with biological entities. These behaviors may be used to perform tasks such as rotation or linear translation in the vertical and horizontal directions. Yet another system builds "curtains". Behaviors are controlled by a complex network of physical and chemical processes that are organized in space and time. The type of dynamical behavior is determined by the chemical composition of the cell and the environment. By studying these systems we may learn general rules for the growth of living entities, or at least about the spontaneous growth of complex chemical structures. Understanding and mastering the synthesis of these systems may lead to new technologies where complex structures are grown rather than assembled.