Research on solar cells with three-dimensional (3D) organic-inorganic perovskites has attracted a great deal of interest within the photovoltaics (PV) community. This is largely due to the rapid increase in power conversion efficiency (PCE) perovskites have enabled in recent years for solar cells. Within single junctions, the PCE has gone up from a few percent (%) in 2006, to more than 25.7% presently, with methyl-ammonium lead triiodide, i.e., MAPbI3 or specifically CH3NH3PbI3, being a widely studied perovskite composition from the early days. These perovskite solar cells (PSCs) have risen to prominence rapidly, in comparison to prior generation technologies such as small molecule, polymer, and CdTe and CZTSSe solar cells. Although PSCs have shown great promise in attaining high PCE, there are nonetheless, major materials-related issues related to stability which present some significant bottlenecks in commercializing this technology. In this work, we provide an overview of the operational characteristics and theory of solar cells, followed by some historical context. The basics of the materials structure and crystallinity, specifically related to 3D perovskites, are then discussed, where we move onto the lower dimensionality formulations, namely, the two-dimensional (2D) and one-dimensional (1D) perovskites, which have the potential to help alleviate some of the stability issues plaguing 3D perovskites. Within the 2D perovskites, we delve more deeply into the material characterization and optoelectronic transport characteristics of these solution-processed 2D photo-absorbers in a photodetector platform, which influences their optical absorption character in the solar cell framework as well.