The first successful spectrum of a galaxy, M31, was obtained in 1898 and published in a two-page paper in the young Astrophysical Journal (Scheiner 1899). Thus the first century of galaxy spectroscopy and the first century of the Astrophysical Journal are almost coincident; I celebrate both in this paper. I describe the very early history of the determination of internal kinematics in spiral galaxies, often by quoting the astronomers' own published words. By mid-century, observations with improved optical and radio telescopes offered evidence that much of the matter in a galaxy is dark. As the century ends, research interests have enlarged to include study of spheroidal and disk galaxies with complex nuclear (and other) kinematics. These complicated velocity patterns are understood as the result of interactions, acquisitions, and mergers, and offer clear evidence of the important role of gravitational effects in galaxy evolution.