We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential non-relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed, and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, non-relativistic sum rules, inclusive decays, and electromagnetic threshold production. © 2011 Elsevier B.V. All rights reserved.