Employing sunlight to produce electrical energy has been demonstrated to be one of the most promising solutions to the world’s energy crisis. The device to convert solar energy to electrical energy, a solar cell, must be reliable and cost-effective to compete with traditional resources. This paper reviews many basics of photovoltaic (PV) cells, such as the working principle of the PV cell, main physical properties of PV cell materials, the significance of gallium arsenide (GaAs) thin films in solar technology, their prospects, and some mathematical analysis of p-n junction solar cells. Furthermore, the paper presents the standard model of solar cells with the application of this model to different PV technologies together with the main findings. Moreover, the paper explores the role of numerical and mathematical modelling of PV cells by MATLAB/Simulink and COMSOL in evaluating the power conversion efficiency (PCE) of the PV cells and determining the main parameters affecting the power output at various conditions.