Although known since the late 19th century, organic-inorganic perovskites have recently received extraordinary research community attention because of their unique physical properties, which make them promising candidates for application in photovoltaic (PV) and related optoelectronic devices. This review will explore beyond the current focus on three-dimensional (3-D) lead(II) halide perovskites, to highlight the great chemical flexibility and outstanding potential of the broader class of 3-D and lower dimensional organic-based perovskite family for electronic, optical, and energy-based applications as well as fundamental research. The concept of a multifunctional organic-inorganic hybrid, in which the organic and inorganic structural components provide intentional, unique, and hopefully synergistic features to the compound, represents an important contemporary target.