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Whenever a compound crystal is cut normal to a randomly chosen direction, there is an overwhelming probability that the resulting surface corresponds to a polar termination and is highly unstable. Indeed, polar oxide surfaces are subject to complex stabilization processes that ultimately determine their physical and chemical properties. However, owing to recent advances in their preparation under controlled conditions and to improvements in the experimental techniques for their characterization, an impressive variety of structures have been investigated in the last few years. Recent progress in the fabrication of oxide nano-objects, which have been largely stimulated by a growing demand for new materials for applications ranging from micro-electronics to heterogeneous catalysis, also offer interesting examples of exotic polar structures. At odds with polar orientations of macroscopic samples, some smaller size polar nano-structures turn out to be perfectly stable. Others are subject to unusual processes of stabilization, which are absent or not effective in their extended counterparts. In this context, a thorough and comprehensive reflexion on the role that polarity plays at oxide surfaces, interfaces and in nano-objects seems timely.This review includes a first section which presents the theoretical concepts at the root of the polar electrostatic instability and its compensation and introduces a rigorous definition of polar terminations that encompasses previous theoretical treatments; a second section devoted to a summary of all experimental and theoretical results obtained since the first review paper by Noguera (2000 J. Phys.: Condens. Matter 12 R367); and finally a discussion section focusing on the relative strength of the stabilization mechanisms, with special emphasis on ternary compound surfaces and on polarity effects in ultra-thin films. [ABSTRACT FROM AUTHOR]