Perovskite solar cells (PSCs) are attracting attention as the most promising next-generation solar cells, recording high efficiency (25.7%) comparable to silicon solar cells. However, perovskite solar cells have difficulties in commercialization because of their low moisture and thermal stability. In particular, 2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenyl-amine)9,9′-spirobifluorene (spiro-OMeTAD) is a representative hole-transporting material (HTM), but it has inherently low hole mobility, so it is doped with dopants such as bis(trifluoromethane)sulfonimide lithium salt (Li-TFSI) and 4-tert-butylpyridine (tBP), which decrease the moisture and heat stability of the device. Therefore, for the commercialization of PSCs, the development of HTMs that make PSCs more efficient and stable is becoming more important. This paper summarizes and discusses recent research progress on efficient and stable devices based on HTMs utilizing spiro-OMeTAD, small molecules, polymers, and functional polymers. In particular, the focus was on polymeric HTMs and functional polymeric HTMs. We believe that this review will provide an accurate analysis of the research trend in HTMs and many insights for designing new HTMs and device systems for the commercialization of PSCs.