Owing to the persisting hype in pushing toward global carbon neutrality, the study scope of atmospheric science is rapidly expanding. Among numerous trending topics, energy meteorology has been attracting the most attention hitherto. One essential skill of solar energy meteorologists is solar power curve modeling, which seeks to map irradiance and auxiliary weather variables to solar power, by statistical and/or physical means. In this regard, this tutorial review aims to deliver a complete overview of those fundamental scientific and engineering principles pertaining to the solar power curve. Solar power curves can be modeled in two primary ways, one of regression and the other of model chain. Both classes of modeling approaches, alongside their hybridization and probabilistic extensions, which allow accuracy improvement and uncertainty quantification, are scrutinized and contrasted thoroughly in this review.