The cultivation of plant cells in large-scale bioreactor systems has long been considered a promising alternative for the overexploitation of wild plants as a source of bioactive phytochemicals. This idea, however, faced multiple constraints upon realization, resulting in very few examples of technologically feasible and economically effective biotechnological companies. The bioreactor cultivation of plant cells is challenging. Even well-growing and highly biosynthetically potent cell lines require a thorough optimization of cultivation parameters when upscaling the cultivation process from laboratory to industrial volumes. The optimization includes, but is not limited to, the bioreactor’s shape and design, cultivation regime (batch, fed-batch, continuous, semi-continuous), aeration, homogenization, anti-foaming measures, etc., while maintaining a high biomass and metabolite production. Based on the literature data and our experience, the cell cultures often demonstrate cell line- or species-specific responses to parameter changes, with the dissolved oxygen concentration (pO2) and shear stress caused by stirring being frequent growth-limiting factors. The mass transfer coefficient also plays a vital role in upscaling the cultivation process from smaller to larger volumes. The Experimental Biotechnological Facility at the K.A. Timiryazev Institute of Plant Physiology has operated since the 1970s and currently hosts a cascade of bioreactors from the laboratory (20 L) to the pilot (75 L) and a semi-industrial volume (630 L) adapted for the cultivation of plant cells. In this review, we discuss the most appealing cases of the cell cultivation process’s adaptation to bioreactor conditions featuring the cell cultures of medicinal plants Dioscorea deltoidea Wall. ex Griseb., Taxus wallichiana Zucc., Stephania glabra (Roxb.) Miers, Panax japonicus (T. Nees) C.A.Mey., Polyscias filicifolia (C. Moore ex E. Fourn.) L.H. Bailey, and P. fruticosa L. Harms. The results of cell cultivation in bioreactors of different types and designs using various cultivation regimes are covered and compared with the literature data. We also discuss the role of the critical factors affecting cell behavior in bioreactors with large volumes.