Robustness is typically understood as an ability of adaptive beamforming algorithm to achieve high performance in the situations with imperfect, incomplete, or erroneous knowledge about the source, propagation media, and antenna array. It is also desired to achieve high performance with as little as possible prior information. In the last decade, several fruitful principles to minimum variance distortionless response (MVDR) robust adaptive beamforming (RAB) design have been developed and successfully applied to solve a number of problems in a wide range of applications. Such principles of MVDR RAB design are summarized here in a single paper. Prof. Gershman has actively participated in the development and applications of a number of such MVDR RAB design principles. ► This is a tutorial paper on principles of minimum variance robust adaptive beamforming design. ► Recent progress in the field was facilitated by the advances in convex optimization. ► The extensions to general rank signal model and broadband case are considered. ► Prof. Alex B. Gershman contributed in developing a number of such principles.