The review deals with a special kind of gas-filled polymeric materials: the syntactic polymer foams, or spheroplastics, consisting of a polymer matrix and a hollow spherical filler. The survey covers the following aspects: preparation and properties of polymeric hollow micro- and macrospheres; physical principles of syntactic foam formation: rheology, regulation of apparent density, space factor and packing of syntactic compositions; chemical and technological principles of formation; preparation of syntactic foams based on epoxy, polyester, phenol, polyimide, and other resins, as well as the newest types of foams — prepregs, poly-phase structures, elastomeric and reinforced foams. The specificity of physical properties and methods of calculation of strength parameters are discussed. Attempts are made to evaluate the effect and contribution of size and packing of spheres on the principal physical properties. The main applications and trends of syntactic foams are outlined.