Sasakian manifolds are considered by many as odd-dimensional counterparts of Kähler manifolds. We start with basic definitions and then continue with the fundamental geometric and topological properties of Sasakian manifolds. Some of these properties are obstructions to the existence of a Sasakian structure on a contact or more general odd-dimensional manifold. These obstructions are the fundamental tools in the proofs of the existence or non-existence results for given classes of odd-dimensional manifolds. Sasakian manifolds can be also investigated as foliated manifolds. Some of the well-known results are, in fact, true for a larger class of foliated manifolds, i.e., transversely Kähler isometric flows. Finally, we will present some applications of Sasakian manifolds.