An efficient algorithm is described for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, the memory requirements are identical with the zero-padding technique, with the important distinction that the additional work memory need not be contiguous with the data. This decoupling of the data and work arrays dramatically reduces the memory and computation time required to evaluate higher-dimensional in-place convolutions. The technique also allows for the efficient dealiasing of the hyperconvolutions that arise on Fourier transforming cubic and higher powers. We discuss recent advances in the parallel implementation of implicit dealiasing that exploit the possibility of overlapping computation with communication.