Ultrafast nonlinear optics deals with frequency mixing processes on timescales as short as several hundred femtoseconds. Novel applications in quantum optics demand advanced devices tailored for specific tasks. This thesis addresses the concept of dispersion engineering, in which the dispersive properties of nonlinear materials are used to control the functional properties of nonlinear devices. The concept is reviewed in the light of previously developed processes, namely the quantum pulse gate (QPG) and parametric down-conversion (PDC) sources and novel applications are demonstrated. These applications include measurement and manipulation of single-photon pulses. Bandwidth compression and difference-frequency generation pulse shaping, where the spectrum of photons is efficiently reshaped, is demonstrated and the low-noise properties of the process are verified. Cross-correlation measurements on PDC photons are performed and their implication on these quantum states of light is outlined. Spectral domain dispersion engineering is extended to the application of time-domain upconversion. Here, the dispersive, i.e. spectral properties of nonlinear materials are linked to their impact on the temporal structure of the converted pulses. The resulting formalism is used to develop a time domain upconverter capable of reliably imaging femtosecond to picosecond pulses. In a proof-of-principle experiment, sufficient efficiency for single-photon level operation is demonstrated.