The article provides an extensive review on the topic of microwave and millimeter‐wave power combiners and dividers. Because many power combining and dividing structures can be used interchangeably, the review focuses on power combiners. It commences with an introduction of power combining principles and grouping of power combiners into suitable categories. The main categories considered here include circuit‐level (both resonant and nonresonant type) and space‐level power combiners. Next, operation and fundamental characteristics of circuit and space‐level combiners, which have been presented in the microwave literature, are thoroughly explained. In the subsequent sections, analysis methods for power combiner/divider structures are described. They concern both circuit and electromagnetic field approaches. The use of state‐of‐the art computer software for the analysis of power combining/dividing structures is also covered. The last section of the article is concerned with applications of power combiner/dividers in modern communication and radar systems. Examples of most impressive power combiners of solid‐state devices, in terms of an achieved output power level or highest frequency of operation, are presented. The review concludes with remarks on recent progress in the field of space‐level combiners.