Chirped quasi-phasematching (QPM) optical devices offer the potential for ultrawide bandwidths, high conversion efficiencies, and high amplification factors across the transparency range of QPM media. In order to properly take advantage of these devices, apodization schemes are required. We study apodization in detail for many regimes of interest, including low-gain difference frequency generation (DFG), high-gain optical parametric amplification (OPA), and high-efficiency adiabatic frequency conversion (AFC). Our analysis is also applicable to secondharmonic generation, sum frequency generation, and optical rectification. In each case, a systematic and optimized approach to grating construction is provided, and different apodization techniques are compared where appropriate. We find that nonlinear chirp apodization, where the poling period is varied smoothly, monotonically, and rapidly at the edges of the device, offers the best performance. We consider the full spatial structure of the QPM gratings in our simulations, but utilize the first order QPM approximation to obtain analytical and semianalytical results. One application of our results is optical parametric chirped pulse amplification; we show that special care must be taken in this case to obtain high gain factors while maintaining a flat gain spectrum.