Since 1978, when BL Lac objects and violently variable quasars were married to become “blazars”, physical interpretations of the phenomenon have evolved. Remarkably, though, the general picture of relativistic jets beaming their radiation in our direction, proposed that year by Blandford and Rees, remains intact. The main stress on theoretical models has come from observations that reveal ever more extreme variability requiring rampant particle acceleration on time-scales of minutes, often parsecs away from the central black hole. Here the author reviews many of the observations and theoretical ideas that have shaped his studies of blazars over about 40 years. This leads to his preferred scenario that blazar jets contain a helical magnetic field close to the black hole, turbulent plasma on parsecs scales, and both standing and moving shock waves. Particle acceleration can then occur in multiple stages involving the second-order Fermi process, magnetic reconnections, and modest jumps in energy at shock fronts. The most extreme variability, as well as brightness temperatures ~100 times the inverse Compton limit, probably require occasional exceptionally high bulk Lorentz factors. These can result, for example, from supersonic, relativistic turbulence, or ultra-relativistic flows propelled from sites of magnetic reconnection. Future efforts in these and other areas can determine whether these potential solutions are valid.