We have carried out temperature- and pressure-dependent Raman and x-ray measurements on single crystals of Tb₂Ti₂O₇. We attribute the observed anomalous temperature dependence of phonons to phonon-phonon anharmonic interactions. The quasiharmonic and anharmonic contributions to the temperature- dependent changes in phonon frequencies are estimated quantitatively using mode Grüneisen parameters derived from pressure-dependent Raman experiments and bulk modulus from high-pressure x-ray measurements. Further, our Raman and x-ray data suggest a subtle structural deformation of the pyrochlore lattice at ~9 GPa. We discuss possible implications of our results on the spin-liquid behavior of Tb₂Ti₂O₇.