Ultrafast imaging based on coherent plane-wave compounding is one of the most important recent developments in medical ultrasound. It significantly improves image quality and allows for much faster image acquisition. This method, however, incurs severe computational loads that create a major bottleneck in its implementation using existing commercial systems. To overcome this limitation we translate the beamforming, which is the basic processing step, to the frequency domain. As a result the computations can be carried out much more efficiently and using less data samples. To this end, we extend the frequency domain beamforming (FDBF) framework developed recently for the focused imaging mode to plane-wave imaging. We show that the core of FDBF, the relationship between the beam and the detected signals in the frequency domain, holds and can be implemented efficiently by introducing an appropriate approximation. We also show that dynamic aperture and apodization, crucial for image quality improvement, can be applied directly in frequency as a part of FDBF. The translation of beamforming into the frequency domain allows for data rate reduction by eliminating oversampling, required by digital implementation of beamforming in time. As a result the signals are sampled and processed at their effective Nyquist rate, leading to a 4-fold reduction in the number of samples.