A number of liquid phase epitaxy (LPE) related growth methods have been investigated. These hybrid-LPE processes enable high rate 'liquid assisted' growth of epitaxial YBa 2 Cu 3 O 7 films without the many disadvantages of classical LPE. Growth occurs by diffusive transport of Y through a thin liquid flux layer. This layer may be pre-deposited onto the substrate by various means including vacuum and non-vacuum techniques, or deposited at the growth temperature. The composition of the liquid layer is maintained during film growth by feeding YBa 2 Cu 3 O 7 , or the separate components, either from the vapour or by a powder route. Growth rates up to 10 nm s −1 have been demonstrated. Deposition of c-axis oriented epitaxial YBa 2 Cu 3 O 7 is reported on both seeded and non-seeded substrates; the process is tolerant of a high substrate mismatch. Films 1-2 µm thick with T c ∼ 90 K and a critical current density J c > 2 MA cm −2 have been grown on a range of single crystal substrates as well as on buffered textured metallic tapes. The mechanism of nucleation and growth from a thin liquid layer is described within the general theoretical framework of crystal growth. Particular features of the growth are the short time constant for equilibration of transients in the deposition conditions, the wide range of relative supersaturation spanned by the process, and dominance of interface kinetic effects compared to volume diffusion in the liquid flux.