  Koszul and homogeneous Koszul algebras were defined by Priddy in
\cite{Priddy1970}. There exist some relations between these algebras and the
skew PBW extensions introduced in \cite{LezamaGallego}. In this paper we give
conditions to guarantee that skew PBW extensions over fields are Koszul or
homogeneous Koszul. We also show that a constant skew PBW extension of a field
is a PBW deformation of its homogeneous version.
