Third-order nonlinearity is the dominant nonlinear response in centrosymmetric materials such as silicon, silicon dioxide and silicon nitride. To enhance light-matter interactions, high Q microresonators can be employed. In this talk, we will discuss the use of third-order nonlinearity in high Q silicon nitride microresonators for several important applications. The first example is focused on the design and demonstration of octave-spanning frequency combs. Optimized dispersion design not only allows us to obtain an octave span of spectrum (1um to 2um), but also enables two harmonically linked dispersive wave emission which is particularly useful for frequency self-referencing. In the second example, we shift our focus from the classical domain to the quantum domain, where quantum states of light and quantum frequency conversion are both achieved by the same third-order nonlinearity of SiN. Specifically, one photon from a quantum-correlated microresonator photon pair source is frequency shifted by four-wave mixing Bragg scattering in a second microresonator, without degrading the level of quantum correlation. With the developed technologies, we demonstrate tunable quantum interference of the initially non-degenerate photons comprising the pair, and observe the quantum beat of single photons as the photon frequencies are tuned across each other. Our work showcases the versatility of the nanophononics for both classical and quantum information processing.