This article overviews the current state and prospects of the concept of advanced single-molecule magnets (SMMs) based on low-spin (S = 1/2) pentagonal-bipyramidal (PBP) 4d3 and 5d3 complexes with unquenched orbital angular momentum. This approach is based on the unique property of PBP 4d3 and 5d3 complexes to cause highly anisotropic spin coupling of perfect uniaxial symmetry, -JzSziSzj - Jxy(SxiSxj + SyiSyj), regardless of the local geometric symmetry. The M(4d/5d)-M(3d) exchange-coupled pairs in the apical positions of the PBP complexes produce Ising-type exchange interactions (|Jz| > |Jxy|), which serve as a powerful source of uniaxial magnetic anisotropy of a SMM cluster. In polynuclear heterometallic 4d/5d-3d complexes embodying PBP 4d/5d units and high-spin 3d ions, anisotropic Ising-type exchange interactions produce a double-well potential with high energy barriers Ueff, which is controlled by the anisotropic exchange parameters Jz, Jxy. Theoretical analysis shows that the barrier is proportional to the difference |Jz - Jxy| and to the number n of the apical 4d/5d-3d pairs in a SMM cluster, Ueff ∝ |Jz - Jxy|n, which provides an opportunity to scale up the barrier Ueff and blocking temperature TB up to the record values. A novel family of 4d/5d complexes with forced PBP coordination provided by structurally rigid planar pentadentate Schiff-base ligands in the equatorial plane is discussed as a better alternative to the cyanometallates. The possibility of a significant increase in the anisotropic exchange parameters Jz, Jxy in PBP complexes with monoatomic apical μ-bridging ligands is examined. The basic principles of molecular engineering the highest barrier through anisotropic exchange interactions of PBP 4d/5d complexes are formulated. The theoretical and experimental results taken together indicate that the concept of high-performance SMMs based on 4d/5d PBP complexes with unquenched orbital angular momentum is an attractive alternative to the currently dominant lanthanide-based SMM strategy.