This thesis comprises three major parts relating to the electron and phonon dynamics in nanos-tructures. In the rst part, a nite temperature Green's function theory for spherically symmetric systems is advanced, in which a self-consistent dressed random phase approximation is proposed. The nite element method is generalized to solve the Dyson equations for the Green's function and the screening potential. The linear response theory is then used to obtain the electron polarizability. By the Pade approximant, the imaginary Matsubara frequency dependence is analytically continued to calculate the polarizability in the real frequency domain This approach has been applied to Gold and Sodium nanosphere systems. In the second part, a general theoretical technique is developed to describe wave propagation through a curved wire of uniform cross section and lying in a plane, but of otherwise arbitrary shape. The method consists of (i) introducing a local orthogonal coordinate system, the arclength and two locally perpendicular coordinate axes, dictated by the shape of the wire; (ii) rewriting the wave equation of interest in this system; (iii) identifying an eective scattering potential caused by the local curvature; and (iv), solving the associated Lippmann-Schwinger equation for the scattering matrix. We carry out this procedure in detail for the scalar Helmholtz equation with both hard- wall and stress-free boundary conditions, appropriate for the mesoscopic transport of electrons and (scalar) phonons. The results show that, in contrast to charge transport, curvature only barely suppresses thermal transport, even for sharply bent wires, at least within the two-dimensional scalar phonon model considered. Applications to experiments are also discussed. In the third part, a general method is developed to calculate the net rate of thermal energy transfer between a three-dimensional conductor at temperature Tel and a low-dimensional phonon system at temperature Tph. The main focus and principal result is a calculation of the rate of energy transfer between a clean metal lm of thickness d attached to an insulating, nonpolar semi-innite substrate. The conventional deformation-potential is employed to describe the electron-phonon 5 scattering. A low-temperature crossover from the familiar Ttemperature dependence to a strong 6 Tlog T scaling is predicted. Comparison with the existing experiments suggests a widespread breakdown of the standard model of electron-phonon thermalization in supported metallic thin lms.