The coupling between lattice and electronic degrees of freedom in materials is at the heart of a variety of phenomena, including superconductivity, heat and charge transport, indirect optical absorption, and the temperature dependence of electronic structure. Density functional theory (DFT) calculations of electron-phonon coupling have proven to be powerful tools for predicting and elucidating these phenomena. We have developed new DFT-based implementations for calculating electron-phonon coupling relevant to two novel applications. The first is the calculation of Shockley-Read-Hall (SRH) recombination of carriers at point defects. SRH is a detrimental, efficiency-lowering process in light-emitting diodes and solar cells; it is often mediated by phonons, so electron-phonon coupling at point defects must be treated. The second application is for determining flexoelectric coefficients. Flexoelectricity refers to the polarization induced in a material by the application of a strain gradient. It is a universal effect in all insulators, and has implications for electronic devices. Computing the flexoelectric response of a material is also an electron-phonon coupling problem, since strain gradients can be treated as very-long-wavelength acoustic phonons. I will describe our first-principles methodologies for calculating flexoelectricity and SRH recombination, and give examples of calculations for technologically interesting materials.