  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.
