Owing to their high efficiency, low‐cost solution‐processability, and tunable bandgap, perovskite solar cells (PSCs) made of hybrid organic‐inorganic perovskite (HOIP) thin films are promising top‐cell candidates for integration with bottom‐cells based on Si or other low‐bandgap solar‐cell materials to boost the power conversion efficiency (PCE) beyond the Shockley‐Quiesser (S‐Q) limit. In this review, recent progress in such tandem solar cells based on the emerging PSCs is summarized and reviewed critically. Notable achievements for different tandem solar cell configurations including mechanically‐stacked, optical coupling, and monolithically‐integrated with PSCs as top‐cells are described in detail. Highly‐efficient semitransparent PSC top‐cells with high transmittance in near‐infrared (NIR) region are critical for tandem solar cells. Different types of transparent electrodes with high transmittance and low sheet‐resistance for PSCs are reviewed, which presents a grand challenge for PSCs. The strategies to obtain wide‐bandgap PSCs with good photo‐stability are discussed. The PCE reduction due to reflection loss, parasitic absorption, electrical loss, and current mismatch are analyzed to provide better understanding of the performance of PSC‐based tandem solar cells. Recent progress in the research and development PSCs‐based tandem solar cells is reviewed. Different architectures, such as monolithically‐integrated, mechanically‐stacked, and optically‐coupled tandems are discussed. The development of transparent electrodes and wide bandgap PSCs are presented. The power losses in the tandem solar cells are analyzed.