In this thesis, we studied two phenomena involved with the magnon-electron scattering due to the s-d interaction: the thermal spin injection and the magnetoresistance in the ferromagnetic materials. The spin current injection and spin accumulation near a ferromagnetic insulator (FI)/nonmagnetic metal (NM) bilayer film under a thermal gradient is investigated theoretically. By using the Fermi golden rule and the Boltzmann equations, we find that FI and NM can exchange spins via interfacial electron-magnon scattering which is described by the s-d interaction because of the imbalance between magnon emission and absorption caused by either the deviation of the magnon number from the equilibrium Bose-Einstein distribution, or difference in magnon temperature and electron temperature. When two heat baths are attached to the bilayer structure longitudinally (the heat flows perpendicular to the interface), a temperature distribution is determined by the thermal parameters and the sizes of the materials. A linear-response transport theory shows that a temperature gradient in FI and/or a temperature difference across the FI/NM interface generates a spin current which carries angular momenta parallel to the magnetization of FI from the hotter side to the colder one. Interestingly, the spin current induced by a temperature gradient in NM is negligibly small due to the nonmagnetic nature of the non-equilibrium electron distributions. The results agree well with all existing experiments. Such spin current across the interface is converted into the spin current carried by conduction electrons in the nonmagnetic metal layer, which can be affected by the spin-orbital coupling and converted to an electric voltage along a direction perpendicular to both the thermal gradient or the magnetization orientation. And the value of such voltage is determined by the spin Hall angle and other parameters. Such heat-to-electricity conversion devices can be used in the area of waste heat recovery. Besides of other possible applications, the results should be useful in extracting material parameters such as spin Hall angle from experimental measurements. Another phenomena involved the magnon-electron scattering is the intrinsic magnonic magnetoresistance (MMR) of magnetic metals. To get a pure results, we limited our study in the nanowires. We theoretically investigated the MR due to magnon scattering in metals. MMR at room temperature is found to be linear in magnetic field along the magnetization direction for typical ferromagnetic materials. The slope can be either positive or negative, depending on whether the field is parallel or antiparallel to the magnetization direction. Surprisingly, the MMR increases (decreases) with temperature below (above) a critical temperature, determined by the ratio of resistivity from impurity scattering and the thermal resistivity coefficient due to the electron-magnon scattering. The comparison between the theoretical results and recent experiment (PRL 107, 136605 (2011)) is also made.