Multi-junction (tandem) solar cells (TSCs) consisting of multiple light absorbers with considerably different band gaps show great potential in breaking the Shockley-Queisser (S-Q) efficiency limit of a single junction solar cell by absorbing light in a broader range of wavelengths. Perovskite solar cells (PSCs) are ideal candidates for TSCs due to their tunable band gaps, high PCE up to 25.2%, and easy fabrication. PSCs with high PCEs are typically fabricated via a low temperature solution method, which are easy to combine with many other types of solar cells like silicon (Si), copper indium gallium selenide (CIGS), narrow band gap PSCs, dye-sensitized, organic, and quantum dot solar cells. As a matter of fact, perovskite TSCs have stimulated enormous scientific and industrial interest since their first development in 2014. Significant progress has been made on the development of perovskite TSCs both in the research laboratories and industrial companies. This review will rationalize the recent exciting advancement in perovskite TSCs. We begin with the introduction of the historical development of TSCs in a broader context, followed by the summary of the state-of-the-art development of perovskite TSCs with various types of device architectures. We then discuss the strategies for improving the PCEs of perovskite TSCs, including but not limited to the design considerations on the transparency of perovskite absorbers and metal electrodes, protective layers, and recombination layers (RLs)/tunnel junctions (TJs), with a particular focus on the band gap tuning and thickness adjustment of active layers. We subsequently introduce a range of measurement techniques for the characterization of perovskite TSCs. We also cover other core issues related to the large-scale applications and commercialization. Finally, we offer our perspectives on the future development of emerging photovoltaic technologies as the device performance enhancement and cost reduction are central to almost any type of solar cell applied in the perovskite TSCs.