The voltage-gated potassium channel KCNQ1 (Kv7.1) is modulated by KCNE1 (minK) to generate the I Ks current crucial to heartbeat. Defects in either protein result in serious cardiac arrhythmias. Recently developed structural models of the open and closed state KCNQ1/KCNE1 complexes offer a compelling explanation for how KCNE1 slows channel opening and provides a platform from which to refine and test hypotheses for other aspects of KCNE1 modulation. These working models were developed using an integrative approach based on results from nuclear magnetic resonance spectroscopy, electrophysiology, biochemistry, and computational methods—an approach that can be applied iteratively for model testing and revision. We present a critical review of these structural models, illustrating the strengths and challenges of the integrative approach.