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This is part of the recording of the IEEE AESS online distinguished lecture I gave in early 2024. The following is the abstract: Target direction finding and localization is an important problem in radar detection and estimation based on antenna arrays. Normally a full measurement (including both phase and magnitude) of the received signals is needed for effective detection and estimation and many classic direction finding algorithms are based on this assumption, such as MUSIC and ESPRIT. However, this would need prior calibration of the whole array system to remove any possible phase errors present in the measurements, which may not be realistic in many practical scenarios and phase errors are not avoidable as a result. In this talk, a new class of methods and algorithms will be presented for effective target direction finding and localization without relying on the phase information of the received array signals, leading to robust solutions to the problem based on magnitude-only measurements.