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We review here some aspects of our recent works about the geometricengineering of heterotic little string theories using F-theory. Building on theseminal work by Aspinwall and Morrison as well as Intrilligator and Blum, wesolve some longstanding open questions thanks to recent progress in ourunderstanding of 6D (1,0) theories and their generalized symmetries. On thegeometry side, these systems correspond to non-compact elliptically fiberedCalabi-Yau varieties that must admit the structure of an elliptic K3 fibration.From fiberwise F-theory/Heterotic duality the K3 plays a central role - itdetermines the 6D flavor group, as well as different T-dual LSTs viainequivalent elliptic fibration structures. The geometries we obtain are somefiner versions of Kulikov degenerations: the point where the K3 fiberdegenerates is the locus where the LST arises. This structure serve on one handto check our field theory predictions on LST dualities via the match of Coulombbranch dimension, flavor symmetries, and 2-group structure constants, and alsoon the other hand to deduce novel LST models and their networks of dualities,thus allowing exploring non-geometric Heterotic regimes.

6D Heterotic Little String Theories and F-theory Geometry: An Introduction