Magnetic anisotropy of R2T14B (R=rare earth and T=transition metals such as Fe and Co) and partly substituted derivatives thereof are studied over a range of temperatures. The salient features are axial anisotropy for Y2Fe14B versus planar anisotropy for Y2Co14B. Only R with negative second-order Stevens’ factor (such as Nd) will show axial anisotropy contributions near room temperature. However, even in this case nonaxial contributions compete at cryogenic temperature, leading to a spin reorientation for R=Nd and Ho with TRs=140 and 62 K, respectively, for the Fe-based compounds. The symbol R is used to amplify the point that the spin reorientation is primarily triggered by an internal competition of R in question. The origin of this anisotropy competition is further illuminated by studies on partly R substituted materials, such as (Nd1−xRx)2Fe14B. Several contributions to the complex situation are considered including: (a) different site contributions (4f, 4g), (b) different order crystal-field terms, such as V02, V22, and V04 on 4f and 4g, (c) relative magnitude of exchange and crystal field, and (d) the trend for smaller R to preferentially occupy the 4f site. Another type of spin reorientation is observed when R and T sublattice anisotropies compete. An example is Er2Fe14B with TR-Ts=326 K. More complex mixed cases are either observed or predicted.