Accumulation of new data on stellar hierarchical systems and the progress in numerical simulations of their formation open the door to genetic classification of these systems, where properties of a certain group (family) of objects are tentatively related to their formation mechanisms and early evolution. A short review of the structure and statistical trends of known stellar hierarchies is given. Like binaries, they can be formed by the disk and core fragmentation events happening sequentially or simultaneously and followed by the evolution of masses and orbits driven by continuing accretion of gas and dynamical interactions between stars. Several basic formation scenarios are proposed and associated qualitatively with the architecture of real systems, although quantitative predictions for these scenarios are still pending. The general trend of increasing orbit alignment with decreasing system size points to the critical role of the accretion-driven orbit migration, which also explains the typically comparable masses of stars belonging to the same system. The architecture of some hierarchies bears imprints of chaotic dynamical interactions. Characteristic features of each family are illustrated by several real systems.