  The time-frequency degree of freedom is a powerful resource for implementing
high-dimensional quantum information processing. In particular,
field-orthogonal pulsed temporal modes offer a flexible framework compatible
with both long-distance fibre networks and integrated waveguide devices. In
order for this architecture to be fully utilised, techniques to reliably
generate diverse quantum states of light and accurately measure complex
temporal waveforms must be developed. To this end, nonlinear processes mediated
by spectrally shaped pump pulses in group-velocity engineered waveguides and
crystals provide a capable toolbox. In this review, we examine how tailoring
the phasematching conditions of parametric downconversion and sum-frequency
generation allows for highly pure single-photon generation, flexible
temporal-mode entanglement, and accurate measurement of time-frequency photon
states. We provide an overview of experimental progress towards these goals,
and summarise challenges that remain in the field.
