The structural properties as well as epitaxial growth peculiarities of thin film silicon-based heterostructures (SBH) are described with emphasis put on MBE growth of these structures. More detailed considerations are presented for the strained-layer Si1-xGex/Si heterostructures. The 4.17% lattice mismatch between Si and Ge is the reason for considering the Si-based heteroepitaxy realised with the Si1-xGex alloy as strained-layer epitaxy. Consequently, the effects of strain on epitaxial growth and on properties of Si1-xGex/Si heterostructures are also described and discussed in this paper. The review is concluded with a discussion on key issues concerning the important 2D layer-by-layer growth mode in strained-layer MBE of SBHs. The considerations are based on current understanding of physical principles of epitaxial growth of these thin film structures.