Lead-based organohalide perovskites have recently emerged as arguably the most promising of all next generation thin film solar cell technologies. Power conversion efficiencies have reached 20% in less than 5 years, and their application to other optoelectronic device platforms such as photodetectors and light emitting diodes is being increasingly reported. Organohalide perovskites can be solution processed or evaporated at low temperatures to form simple thin film photojunctions, thus delivering the potential for the holy grail of high efficiency, low embedded energy, and low cost photovoltaics. The initial device-driven "perovskite fever" has more recently given way to efforts to better understand how these materials work in solar cells, and deeper elucidation of their structure-property relationships. In this Account, we focus on this element of organohalide perovskite chemistry and physics in particular examining critical electro-optical, morphological, and architectural phenomena. We first examine basic crystal and chemical structure, and how this impacts important solar-cell related properties such as the optical gap. We then turn to deeper electronic phenomena such as carrier mobilities, trap densities, and recombination dynamics, as well as examining ionic and dielectric properties and how these two types of physics impact each other. The issue of whether organohalide perovskites are predominantly nonexcitonic at room temperature is currently a matter of some debate, and we summarize the evidence for what appears to be the emerging field consensus: an exciton binding energy of order 10 meV. Having discussed the important basic chemistry and physics we turn to more device-related considerations including processing, morphology, architecture, thin film electro-optics and interfacial energetics. These phenomena directly impact solar cell performance parameters such as open circuit voltage, short circuit current density, internal and external quantum efficiency, fill factor, and ultimately the all-important power conversion efficiency. Finally, we address the key challenges pertinent to actually delivering a new and viable solar cell technology. These include long-term cell stability, scaling to the module level, and the toxicity associated with lead. Organohalide perovskites not only offer exciting possibilities for next generation optoelectronics and photovoltaics, but are an intriguing class of material crossing the boundaries of molecular solids and banded inorganic semiconductors. This is a potential area of rich new chemistry, materials science, and physics.