A Vacuum Insulating Glazing Unit (VIGU) comprises two or more glass lites (panes) spaced apart from one another and hermetically bonded to an edge seal assembly therebetween. The resulting cavity between the lites is evacuated to create at least one insulating vacuum cavity within which are disposed a plurality of stand-off members to maintain separation between the lites. The edge seal assembly is preferably compliant in the longitudinal (i.e., edgewise) direction to allow longitudinal relative motion between the two lites (e.g., from thermal expansion). The longitudinal compliance may be obtained by imprinting a three-dimensional pattern into the edge seal material. The edge seal assembly is preferably bonded to the lites with a first bond portion that is hermetic and a second bond portion that is load-resistant. Methods for producing VIGUs and/or compliant edge seal assemblies and VIGU and edge seal apparatus are disclosed.