Classical hydroboration is the textbook example of an organometallic reaction under rigorous frontier orbital control: a synergetic bonding mode between substrate and reagent evolves into a four‐membered transition state that enforces syn/suprafacial delivery of H−BR2 to the π‐system. This strict stereochemical “law” remained valid for decades, even after the advent of metal‐catalyzed hydroboration. During the last decade, however, numerous possibilities emerged that allow this paradigm to be challenged. Thus, direct trans‐hydroboration of terminal as well as internal alkynes was achieved through radical, ionic, organocatalytic, and metal‐catalyzed manifolds, which are summarized in this review. Among them, pathways involving either metal vinylidenes (Rh, Ir, Ru, Fe) derived from terminal alkynes or metallacyclopropenes (η2‐vinylmetal complexes) derived from an internal triple bond and a [CpXRu]‐based catalyst represent the currently most widely applicable solutions. The latter type of intermediates is also accountable for the equally perplexing gem‐hydroboration of alkynes: geminal delivery of a borane to a triple bond has no precedent in the classical canon. The only forerunner was gem‐hydrogenation, which represents an unconventional yet highly useful entry into discrete ruthenium carbene complexes. The close mechanistic ties between these transformations are outlined, and brief reference is also made to remotely related reactions such as trans‐diboration and trans‐carboboration.