Investigations of multifunctional RAl3(BO3)(4) (R = Y, Pr, Sm-Lu) crystals are divided into three stages: 1962-1972, 1972-1990, 1990 to present, and reviewed step by step. Selective and predominantly unpublished results on high-temperature flux growth (mostly by solution growth on dipped seeds, abbreviated as SGDS method) of these bulk (three-dimensional) crystals and their solid solutions, performed by the author's research group during last decades, are shortly summarized as well. The pursued studies can be considered as a key base for development of highly efficient optical and new laser systems. (C) 2017 Elsevier B.V. All rights reserved.