It is well-known that belief-propagation (BP) decoding of low-density parity-check (LDPC) codes is suboptimal and that the noise threshold of maximum-a-posteriori (MAP) decoding can be better than the BP threshold.  In 2011, Kudekar, Richardson, and Urbanke proved the surprising result that regular LDPC ensembles can be spatially coupled so that the BP noise threshold saturates to the MAP noise threshold of the standard regular ensemble.  This proof was recently simplified by the introduction of a potential function for the dynamics of density evolution.  In this work, we give a short overview of these results and describe how the Maxwell construction of the MAP EXIT curve arises as a natural consequence of minimizing the potential.