Faced with the ever-increasing urban environmental pollution, the electric vehicles (EVs) have received increasing attention in the automotive industry. Lithium-ion batteries, serving as electrochemical power storage, have been extensively used in EVs because of the lightweight, no local pollution and high power density. The increasing awareness on the safe operation and reliability of the battery requires an efficient battery management system (BMS), among the parameters monitored by which, state-of-charge (SOC) is critical in preventing overcharge, deep discharge, and irreversible damage. This article investigates the neural network (NN)-based modeling, learning, and estimation of SOC by comparing two different methodologies, that is, direct structure with SOC as network output and indirect structure with voltage as output. Firstly, the nonlinear autoregressive exogenous neural network (NARX-NN) is introduced, in which SOC is directly deemed as an NN output for learning and estimation. Secondly, a radial basis function (RBF)-based NN with unscented Kalman filter (RBFNN-UKF) is proposed, in which the terminal voltage is used as output. Instead, SOC is deemed as an internal state which would be estimated indirectly based on the feedback error of voltage. Experimental results demonstrate that both estimators can achieve accurate SOC estimation for regular cases, in spite of the inaccurate initial conditions. However, the direct NN structure is revealed as not capable of dealing with the cases with sensor bias, which, however, can be well accommodated in the indirect structure by extending the sensor bias as an augmented state. Benefiting from the uncertainty augmentation and feedback compensation, the indirect RBFNN-UKF shows superiority over the direct estimation in the practical experiments, depicting a promising prospect in the future onboard EV-BMS application.