This article introduces key concepts in Electrochemical-based Control (ECC) systems for batteries, and highlights the fundamentals of battery electrochemistry, state-of-charge/state-of-health (SOC/SOH) estimation, and constrained control. Research on battery SOC/SOH estimation has experienced considerable growth, and can be categorized under equivalent circuit models (ECM) or EChem model-based algorithms. EChem models capture the spatiotemporal dynamics of lithium-ion concentration, electric potential, and intercalation kinetics. The most fundamental reduced EChem model is the single-...