The recent advances in perovskite solar cells (PSCs) created a tsunami effect in the photovoltaic community. PSCs are newfangled high-performance photovoltaic devices with low cost that are solution processable for large-scale energy production. The power conversion efficiency (PCE) of such devices experienced an unprecedented increase from 3.8% to a certified value exceeding 20%, demonstrating exceptional properties of perovskites as solar cell materials. A key advancement in perovskite solar cells, compared with dye-sensitized solar cells, occurred with the replacement of liquid electrolytes with solid-state hole-transporting materials (HTMs) such as 2,2,7,7-tetrakis-(N,N-di-4-methoxyphenylamino)-9,9-spirobifluorene (Spiro-OMeTAD), which contributed to enhanced PCE values and improved the cell stability. Following improvements in the perovskite crystallinity to produce a smooth, uniform morphology, the selective and efficient extraction of positive and negative charges in the device dictated the PCE of PSCs. In this Review, we focus mainly on the HTMs responsible for hole transport and extraction in PSCs, which is one of the essential components for efficient devices. Here, we describe the current state-of-the-art in molecular engineering of hole-transporting materials that are used in PSCs and highlight the requisites for market-viability of this technology. Finally, we include an outlook on molecular engineering of new functional HTMs for high efficiency PSCs.