The capsule histories of physics that students learn in their physics courses stem basically, I believe, from a linear view of history--that physicists in making fundamental discoveries follow a Royal Road to them, as Hermann von Helmholtz put it in 1892. The actual routes they follow, however, are generally nonlinear, and when historians display these routes to students, they express surprise. Such historical surprises could constitute one or more units of instruction in physics-education or other courses. As illustrations, I discuss historical surprises that I have uncovered in my own researches on Isaac Newton's work on diffraction, Robert A. Millikan's photoelectric-effect experiments, Arthur H. Compton's X-ray scattering experiments, James Chadwick's discovery of the neutron, George Gamow's creation of the liquid-drop model of the nucleus, and Lise Meitner's and Otto Robert Frisch's interpretation of nuclear fission. Teachers and students can discover many more historical surprises as provocative as these by exploring the historical literature.