Andrographis paniculata (AP) is a medicinal plant that is traditionally used in Indian, Chinese, Malay, Thai, and Oriental system of medicines to treat various disorders. AP consists of andrographolide (AD), 14-deoxy-11,12-didehydroandrographolide (DDAD), and neoandrographolide (NAD) as major diterpene lactones which has extremely bitter properties; therefore, AP is commonly called "King of bitters." AD, DDAD, and NAD are reported to possess therapeutic values such as antioxidant, immunostimulatory, hepatoprotective, anti-cancer, anti-inflammatory, anti-rheumatoidal, anti-malarial, anti-leishmanial, anti-fertility, anti-obesity, antipyretic, and antimicrobial attributes. According to the Indian Pharmacopoeia, the leaves and tender shoots of AP yield up to 1%, 0.16%, and 0.11% of AD, DDAD, and NAD, respectively, on a dry-weight basis. However, variability in the accumulation of AD, DDAD, and NAD in plants has been reported with respect to species, genotype, season, phenological stage, plant part used, and geography of a region of cultivation. Therefore, cell and tissue culture systems especially cell, shoot, and adventitious root cultures are explored as alternatives for constant and higher production of AD, DDAD, and NAD. This review explores the prospects of exploiting the plant cell and tissue culture systems for the controlled production of AD, DDAD, and NAD. Various strategies such as elicitation by using biological and chemical elicitors are explored for the enhancement of accumulation of AD, DDAD, and NAD in cell and organ cultures.