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We analyze here some electron properties and lattice dynamics in semiconductor heterostructures, pointing out the dramatic changes relative to the bulk properties due to the existence of the interfaces in these systems. The first part of the study is devoted to the electron scattering phenomena in noninteracting open systems and to the transport properties described in the Landauer-Büttiker formalism. We develop a resonant theory of transport and apply it first to the conductance through a quantum dot embedded in a quantum wire and second to the capacitance of a two dimensional electron gas formed in a MIS-type semiconductor heterostructure. In the second part of the study we illustrate the four major new features of the optical phonon spectra in a strained semiconductor heterostructure in contrast to an unstrained one. The results are particularized for double heterostructures InP/GaAs/InP grown on the faces (001) and (111) of the substrate.