Significant growth in solar photovoltaic (PV) installation has been observed during the last decade in standalone and grid-connected power generation systems. However, the PV system has a non-linear output characteristic because of weather intermittency, which tends to a substantial loss in overall system output. Thus, to optimize the output of the PV system, maximum power point tracking (MPPT) techniques are used to track the global maximum power point (GMPP) and extract the maximum power from the PV system under different weather conditions with better precision. Since MPPT is an essential part of the PV system, to date, many MPPT methods have been developed by various researchers, each with unique features. A Google Scholar survey of the last five years (2015–2020) was performed to investigate the number of review articles published. It was found that overall, seventy-one review articles were published on different MPPT techniques; out of those, only four were on non-uniform solar irradiance, and seven review articles included shading conditions. Unfortunately, very few attempts were made in this regard. Therefore, a comprehensive review paper on this topic is needed, in which almost all the well-known MPPT techniques should be encapsulated in one document. This article focuses on online and soft-computing MPPT algorithm classifications under non-uniform irradiance conditions along with their mathematical expression, operating principles, and block diagram/flow charts. It will provide a direction for future research and development in the field of maximum power point tracking optimization.