We are delighted to present this special issue of Multidimensional Systems and Signal Processing on Array Signal Processing and Systems. Sensor arrays play an important role in spatio-temporal signal processing with applications spanning across multiple fields such as electromagnetic, acoustics, ultrasonic and seismic processing systems. This plethora of possible applications has sparked a large number of new theoretical developments and array processing systems in the last few years.In the field of electromagnetic sensor (antenna) arrays, there is much interest in the electronically-steerable radio-frequency (RF) beams that can be obtained from phased-array antennas. In the microwave bands, phased-array antennas take both analog and digital signal processing approaches, and find applications in wireless base-stations, radar sensors, space communications, and radio telescopes. In the emerging mm-wave regime, modern applications of array processing are of paramount importance for wireless communications. In particular, emerging 5G systems based on massive-MIMO basestations depend on array processing to mitigate the effects of high path loss and blockages in an urban environment. Acoustic sensor (microphone) arrays are extremely useful for audio and multimedia applications, including high-fidelity sound recording, immersive multimedia and augmented/virtual reality. Ultrasound sensor arrays find extensive applications in biomedical engineering where they are used for imaging the human body and in structural health monitoring of airframes B Bin Liao