  We review possible dynamical formation processes for central massive black
holes in dense star clusters. We focus on the early dynamical evolution of
young clusters containing a few thousand to a few million stars. One natural
formation path for a central seed black hole in these systems involves the
development of the Spitzer instability, through which the most massive stars
can drive the cluster to core collapse in a very short time. The sudden
increase in the core density then leads to a runaway collision process and the
formation of a very massive merger remnant, which must then collapse to a black
hole. Alternatively, if the most massive stars end their lives before core
collapse, a central cluster of stellar-mass black holes is formed. This cluster
will likely evaporate before reaching the highly relativistic state necessary
to drive a runaway merger process through gravitational radiation, thereby
avoiding the formation of a central massive black hole. We summarize the
conditions under which these different paths will be followed, and present the
results of recent numerical simulations demonstrating the process of rapid core
collapse and runaway collisions between massive stars.
