Acoustic phonons in quantum wells and quantum wires and various mechanisms of their interaction with electrons have been investigated. The obtained radiation patterns and spectrums for emitted acoustic phonons show that the thermal energy is radiated preferably in the direction of spatial quantization. The interaction of the electrons with confined acoustic phonons in free-standing quantum wells leads to the electron relaxation times having steps on their dependence on electron energy. The temperature dependence of the electron mobility is similar to that described by the Bloch-Grueeneisen formula. Confined optical phonons in low-dimensional structures were shown to have unusual properties and to substantially affect the electron transport. The effects of phonon pumping and phonon drag in double-well tunneling heterostructure and the effect of transverse pattern formation in vertical tunnel transport in double-barrier heterostructure have been predicted and thoroughly investigated. The threshold-type scattering of electrons by acoustic phonons has been demonstrated to result in streaming of electrons in low electric fields and at low lattice temperatures. Photocurrent and excess current noise in quantum well infrared photo detectors has been investigated. The quantum well recharge under the influence of the nonuniform generated charge carriers drastically changes the dependencies of both photoconductive gain and excess current noise gain upon detector parameters.