Abstract
After a short review of the principal theories of spiral structure in galaxies, I describe two new developments. First, it now seems clear that linear theory cannot yield a full description for the development of spiral patterns because N-body simulations suggest that non-linear effects manifest themselves at a relative overdensity of ~2%, which is well below the believed spiral amplitudes in galaxies. Second, I summarize the evidence that some stars in the solar neighborhood have been scattered at an inner Lindblad resonance. This evidence strongly supports a picture of spirals as a recurring cycle of transient instabilities, each caused by resonant scattering by a previous wave.
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