Beamforming is a task in array signal processing, used in radar, sonar, acoustics, astronomy, seismology, communications, medical imaging, and other fields. Researchers from Europe and North America describe recent efforts to devise robust adaptive beamformers to alleviate some of the problems with the task. They discuss how to address the array steering vector uncertainty within a clear theoretical framework, alleviating the finite sample size effect, the signal waveform estimation, constant modulus algorithms, and robust wideband beamforming. Readers are assumed to be practicing, research, or graduate-level student engineers.