  We will discuss in this paper homogeneous locally conformally Keahler (or
shortly homogeneous l.c.K.) manifolds and locally homogeneous l.c.K. manifolds
from various aspects of study in the field of l.c.K. geometry. We will provide
a survey of known results along with some new results and observations; in
particular we make a complete classification of 4-dimensional homogeneous and
locally homogeneous l.c.K. manifolds in terms of Lie algebras.
