Applications in remote inspection and medicine have motivated the recent development of innovative thin, flexible-backboned robots. However, such robots often experience difficulties in maintaining their intended posture under gravitational and other external loadings. Thin-stemmed climbing plants face many of the same problems. One highly effective solution adopted by such plants features the use of tendrils and tendril-like structures, or the intertwining of several individual stems to form braid-like structures. In this paper, we present new plant-inspired robotic tendril-bearing and intertwining stem hardware and corresponding novel attachment strategies for thin continuum robots. These contributions to robotics are motivated by new insights into plant tendril and intertwining mechanics and behavior. The practical applications of the resulting GrowBots is discussed in the context of space exploration and mining operations.