Workpieces are either held on both ends ("between centers") and supported by the motor-driven headstock (Spindelstock) and the passively rotating tailstock (Reitstock). The tailstock can be moved along the lathe bed as the length of the workpiece dictates.
We have the following lathes at the CoMakingSpace:
Many lathes have tailstocks with Morse taper fittings - a quick-change conical connection that provides very good holding force by its large surface contact area. 
Drill chucks and collets are among the accessories one could mount using this taper.