Applying the results and techniques of skew PBW extensions developed in the specialized literature, in the present project we want to investigate connections between skew PBW extensions and some rings and algebras arising from non-commutative algebraic geometry. The objects to be considered here correspond to some of new trends in Noncommutative Algebra and Algebraic Geometry identified recently (October-November, 2012) in a workshop organized by MSRI at Banff International Research Station (BIRS) in Alberta, Canada. Three of most relevant topics studied in this workshop were: (i) Hopf algebra actions on filtered algebras (ii) Auslander-Gorenstein rings, Artin-Schelter regular algebras and W-algebras (iii) Skew Calabi-Yau algebras. We will investigate the relationship between skew PBW extensions and these recent classes of rings and algebras.