  This is an expository review paper elaborating on the proof of the martingale
functional central limit theorem (FCLT). This paper also reviews tightness and
stochastic boundedness, highlighting one-dimensional criteria for tightness
used in the proof of the martingale FCLT. This paper supplements the expository
review paper Pang, Talreja and Whitt (2007) illustrating the ``martingale
method'' for proving many-server heavy-traffic stochastic-process limits for
queueing models, supporting diffusion-process approximations.
