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, −J_zS^z_iS^z_j − J_xy(S^x_iS^x_j + S^y_iS^y_j), 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 (|J_z| > |J_xy|), 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 U_eff, which is controlled by the anisotropic exchange parameters J_z, J_xy. Theoretical analysis shows that the barrier is proportional to the difference |J_z − J_xy| and to the number n of the apical 4d/5d–3d pairs in a SMM cluster, U_eff ∝ |J_z − J_xy|n, which provides an opportunity to scale up the barrier U_eff and blocking temperature T_B 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 J_z, J_xy 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.