Here, we collect a majority of known results on the problem of constructing symplectic manifolds with uo Kahlerian structure. With this in mind, uilinanifolds, solvmanifolds, fiber bundles and surgery techniques are discussed. We also present some relevant homotopy theory, e.g. the Dolbeault rational homotopy theory. We give many examples with the aim of claryfying methods of rational homotopy theory to geometers and attracting the attention of "rationalists" to some interesting geometric problems. As an example of the latter, we mention the existence theorems for symplectic fat bundles [ANT, TrK]. This book is meant to be a kind of "bridge" for mathematicians working in two different research areas, so we give proofs (especially geometric ones) of background material where we can while simply providing motivation (and references) where detailed proofs would bring the narrative to a halt. Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory, so we try to present as much of the geometry "hidden" behind algebraic calculations as possible.