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We review the relations between Jordan cells in various branches of physics, ranging from quantum mechanics to massive gravity theories. Our main focus is on holographic correspondences between critically tuned gravity theories in Anti-de Sitter space and logarithmic conformal field theories in various dimensions. We summarize the developments in the past five years, include some novel generalizations and provide an outlook on possible future developments. 36 pp + references, invited review article for J.Phys.A special issue, v2: minor changes, added refs |