Solar cells made from multi- or mono-crystalline silicon wafers are the base of today’s photovoltaics industry. These devices are essentially large-area semiconductor p-n junctions. Technically, solar cells have a relatively simple structure, and the theory of p-n junctions was established already decades ago. The generally accepted model for describing them is the so-called two-diode model. However, the current-voltage characteristics of industrial solar cells, particularly of that made from multi-crystalline silicon material, show significant deviations from established diode theory. These deviations regard the forward and the reverse dark characteristics as well as the relation between the illuminated characteristics to the dark ones. In the recent years it has been found that the characteristics of industrial solar cells can only be understood by taking into account local inhomogeneities of the dark current flow. Such inhomogeneities can be investigated by applying lock-in thermography techniques. Based on these and other investigations, meanwhile the basic properties of industrial silicon solar cells are well understood. This contribution reviews the most important experimental results leading to the present state of physical understanding of the dark and illuminated characteristics of multi-crystalline industrial solar cells. This analysis should be helpful for the continuing process of optimizing such cells for further increasing their energy conversion efficiency.