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On this occasion, I plan to review the evidence that has accumulated from observations and numerical experiments during especially the past decade suggesting that each of these two famous spiral galaxies has been influenced decisively by recent tidal interplay with their respective close neighbors. It is no secret that I am biased: Like a few other astronomers, I have long suspected on dynamical grounds that the magnificent spiral structures which have brought these two galaxies into nearly every introductory textbook (and the latter also onto the cover of the Hubble Atlas) are largely transient wavelike relics of those tidal interactions --- meaning that we would probably have favored some quite different examples had mankind come along just 200 million years earlier or later. But I will try to keep such biases well under control in this review of the recent developments achieved almost entirely by workers other than myself. In other words, this talk will focus not only those portions of the tidal stories which seem well established, but also on some parts which remain shaky.
