  We describe non-Abelian T-dualities for $\mathcal{N} = 2$ two dimensional
gauged linear sigma model (GLSM). We start with the case of left and right $(2,
2)$ supersymmetry (SUSY), $U(1)$ gauge group, and global non-Abelian
symmetries. Our analysis applies to the specialization of the GLSM with the
global group $SU(2)\times SU(2)$, whose original model is the resolved
conifold. We analyze the dual model and compute the periods on the dual
geometry, matching the effective potential for the $U(1)$ gauge field, and
discuss the coincident singularity at the conifold point. We further present
the non-Abelian T-dualization of models with $(0,2)$ SUSY, analyzing the case
of global symmetry $SU(2)$. In this case the full non-Abelian duality can be
solved. The dual geometries with and without non-perturbative corrections to
the superpotential coincide. The structure of the dual non-perturbative
corrections employed are determined based on symmetry arguments. The
non-Abelian T-dualities reviewed here lead to potential new symmetries between
physical theories.
