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The general picture of how thermal AGNs work has become clearer in recent years but major observational puzzles threaten to undermine this picture. These puzzles include AGNs with extremely asymmetric emission line profiles, inconsistent multi-wavelength variability, rapid apparent changes in the sizes of emitting regions and in the direction of gas flow, a curious insensitivity of gas in some narrow velocity ranges to changes in the ionizing continuum, and differing dependences of polarization on gas velocity. It is proposed that all these puzzles can readily be explained by off-axis variability.