  The purpose of this paper is to give a survey of the various versions of
Floer homology for manifolds with contact type boundary that have so far
appeared in the literature. Under the name of ``Symplectic homology'' or
``Floer homology for manifolds with boundary'' they bear in fact common
features and we shall try to underline the principles that unite them. Once
this will be accomplished we shall proceed to describe the peculiarity of each
of the constructions and the specific applications that unfold out of it:
classification of ellipsoids and polydiscs in $\CC^n$, stability of the action
spectrum for contact type boundaries of symplectic manifolds, existence of
closed characteristics on contact type hypersurfaces and obstructions to exact
Lagrange embeddings. The computation of the Floer cohomology for balls in
$\CC^n$ is carried by explicitly perturbing the nondegenerate Morse-Bott
spheres of closed characteristics.
