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Optica 9(2), 197 - 216 (2022). doi:10.1364/OPTICA.449225, Ultrafast lasers reaching extremely high powers within short fractions of time enable a plethora of applications.They grant advanced material processing capabilities, are effective drivers for secondary photonand particle sources, reveal extreme light-matter interactions, and supply platforms for compact acceleratortechnologies, with great application prospects for tumor therapy or medical diagnostics. Many ofthese scientific cases benefit from sources with higher average and peak powers. Following mode-lockeddye and titanium-doped sapphire lasers, broadband optical parametric amplifiers pumped by ytterbium-dopedsolid-state sources have emerged as high peak- and average power, ultrashort pulse lasers. A muchmore power efficient alternative is provided by direct post-compression of high-power diode-pumped ytterbiumlasers, a route, which advanced to another level with the invention of a novel spectral broadeningapproach, the multi-pass cell technique. The method has enabled benchmark results yielding sub-50 fspules at average powers exceeding 1kW, has facilitated femtosecond post-compression at pulse energiesabove 100 mJ and large compression ratios, while staying compact and supporting picosecond to few-cyclepulses. The striking progress of the technique in the past five years puts light sources with tensto hundreds of TW peak and multiple kW of average power in sight - an entirely new parameter regimefor ultrafast lasers. In this review, we introduce the underlying concepts including brief guidelines discussingmulti-pass cell design and implementation. We then present an overview of the achieved performanceswith both bulk and gas-filled multi-pass cells. Moreover, we discuss prospective advancesenabled by this method including in particular opportunities for applications demanding ultrahigh peak power,high repetition rate lasers such as plasma accelerators and laser-driven extreme ultraviolet sources., Published by OSA, Washington, DC