Despite decades of research, the question remains: how do K+-selective channels transport K+ ions across membranes, and at the same time discriminate against Na+ ions, which are as similar as they could be to K+ while not being the same things. Suggestions based on channel size and ligand chemistry have been available since the 1960s, but the determination of K-channel structures has enabled molecularly specific modeling studies of this K+/Na+ selectivity. In the flood of computational studies that have followed, finding consistency in results and interpretations has, however, proven challenging. Molecular insight requires a precise knowledge of how the energetics, structures, dynamics of ions differ between their hydrated and channel-bound states. While first principles quantum mechanical models can yield reliable estimates for relative binding energies, estimates for thermodynamics and ion-binding response are subject to limitations from conformational sampling and system size. In contrast, molecular mechanics models that do not describe electronic polarization explicitly can technically get past sampling/system-size issues, but suffer severely from accuracy. How do we address this dilemma? Polarizable molecular mechanics models are being developed as a compromise between accuracy and efficiency, but are they sufficiently reliable to derive cause-effect relationships? In general, where do we stand in terms of being able to use molecular simulation techniques to understand the design principles underlying the ability of biomolecules to bind ions selectively, and the response of ion binding to biomolecular structure, dynamics and function? In this talk, I’ll present these issues, discuss potential solutions, and provide our perspective on how molecular modeling has advanced our understanding of the specific chemical and structural design elements of biological molecules that enable selective ion transport.