Dynamical evolution in star clusters naturally creates an environment in which interactions among massive stars, binaries, and compact remnants are common. Young clusters may temporarily contain a significant population of stellar black holes, and close encounters and physical collisions among stars in dense cluster cores may lead to the formation of very massive stars and high-mass black holes via runaway merging. Numerical simulations suggest runaway masses in the range commonly cited for intermediate-mass black holes. While our understanding of black hole formation and retention has improved greatly in recent years, substantial uncertainties remain in both the physics of the runaway merger process and the evolution of very massive stars. Direct and indirect observational evidence have been reported for massive black holes in globular clusters, although here too interpretations remain controversial. I examine critically some details of the processes possibly leading to massive black holes in present-day globular clusters, and discuss some observational constraints on the various theoretical scenarios.