The functional properties of materials can be manipulated or modified via both static (e.g. pressure,[24] epitaxial strain,[25] chemical substitution [33, 9]) and dynamic (e.g. light [39]) methods. In perovskites, the functional properties are closely tied to particular structural distortions. I use first-principles density functional theory to explore strain and light control of the functional properties of perovskites via the lattice, that is, through specific changes to the crystal structure induced by optical excitation of phonon modes.I study the effects of optically induced strain on thin films of the well-known multiferroic perovskite BiFeO3. In experiment, ultrafast above-gap excitations of BiFeO3 thin films results in a change in the diffraction intensity proportional to strain, which corresponds to a linear response in tilt angles of the FeO6 octahedra with respect to strain. I calculate the response of these octahedral rotations with respect to strain, supporting the experimental result that octahedral angles can be controlled on the picosecond timescale through coupling to optically induced strain. For the paraelectric perovskite CaTiO3, I explore the viability of an “optical anvil” effect. A thin film of CaTiO3 can be sandwiched by thin films of Ca2RuO4. A light-induced expansion of the sandwiching material applies a compressive strain on CaTiO3 and induces spontaneous polarization. I calculate the effect of strain on the change in polarization of thin films of CaTiO3. My results indicate that depending on the existing biaxial strain of the CaTiO3 thin film, ultrafast light-induced strain allows for control and even suppression of polarization. I also study the nonlinear phononics mechanism, which has been invoked to describe many interesting ultrafast optical experimental results including the ultrafast manipulation of magnetism, light-induced metal-insulator phase transitions, and enhancement of superconductivity.[38, 71, 62, 13] The mechanism involves the coherent optical excitation of infrared-active phonons that, via anharmonic coupling, induce large quasistatic, unidirectional displacement of other lattice degrees of freedom. These structural and functional changes are expected to be transient, lasting approximately the lifetime of the excited IR-active phonon, typically on the order of picoseconds, though examples of long-lived, even metastable, behavior have been reported.[71, 32, 61] I use first-principles theory to explore phonon-phonon scattering in LaAlO3, an important test case for nonlinear phononics due to its structural and functional simplicity.[19, 32, 61] I quantify, up to third-order interactions, the coupling between experimentally observed lattice modes:[32, 61] the infrared-active, Raman-active, and acoustic phonons. Using a phenomenological dynamics model parameterized by first-principles calculations, I then perform theoretical experiments on phonon lifetimes by selective inclusion/exclusion of coupling pathways to gain insight into energy redistributed via lattice degrees of freedom. My results suggest that strong coupling between different degrees of freedom (in this case, strain and particular phonon modes) provides a mechanism through which optically induced phases can have long lifetimes. BAs, a III-V insulator, has thermal conductivity comparable to diamond and higher thermal conductivity than other cubic III-V boron compounds. The origin of this high thermal conductivity has been attributed to the mass ratio and unique chemical bonding character of BAs,[54] both of which give rise to specific features in the phonon dispersion curve that determine the available phonon scattering phase space. I use first-principles density functional theory in combination with the Boltzmann transport equation to systematically explore and disentangle the effects of mass ratio and bonding/chemistry on the thermal conductivity of cubic III-V boron compounds, from c-BN to BSb. Previous work suggests that although the mass ratio of BAs may optimally maximize thermal conductivity,[34] my work shows that the chemical composition of BP may result in higher thermal conductivity. My results create a framework of understanding to further increase thermal conductivity of insulators through modifying bonding and chemistry.