Shortly after the discovery of high‐temperature superconducting (HTS) materials in the late 1980s, it was revealed that grain boundaries in these complex oxides are strong barriers to current flow. This fact has remained one of the most significant challenges to a viable HTS conductor, and necessitated the development of technologies capable of producing biaxially textured substrates in long lengths. Multiple studies have reported that the critical current density (Jc) across grain boundaries in the perovskite‐like superconductor YBa2Cu3O7−x (YBCO) falls off exponentially below the intragrain Jc beyond a critical misorientation angle θc of only ≈2°–3°. Here we review our recent work demonstrating that certain grain boundary geometries permit significant enhancements of Jc well beyond the conventional Jc(θ) limit, and also that the grain boundary structure in YBCO films is tied closely to the films' deposition technique. Pulsed laser deposition, a physical vapor deposition technique, results in a columnar grain structure and planar grain boundaries that exhibit the typical Jc(θ) dependence. Ex situ growth processes, where the YBCO film is converted from a previously deposited precursor, can result in laminar grain growth with highly meandered grain boundaries. These latter grain boundary structures are directly correlated to greatly improved Jc values over a wide range of applied magnetic fields. Consequently, very high Jc values are possible in polycrystalline HTS wire even when significant misorientations between grains are present.