In this work, state of charge (SOC) and state of health (SOH) estimation algorithms for battery management system are proposed and compared. These algorithms are developed on a battery pack designed specifically for light electric vehicle (electric scooter or bicycles) applications. The advanced battery management system is designed in order to evaluate the instantaneous charge available in the battery and at the same time to monitor the slowly varying battery aging parameters. Two SOC estimation algorithms are proposed: an extended Kalman filter (EKF) and an adaptive extended Kalman filter (AEKF). With the adaptive version of Kalman filter a proper value of the model noise covariance is adaptively set using the information coming from the online innovation analysis. In the second part of this paper, a new estimation algorithm based on least squares is proposed to estimate the battery SOH. A general framework for a combined evaluation of SOC/SOH is discussed.