This paper investigates recent research on battery diagnostics and prognostics especially for Lithium-ion (Li-ion) batteries. Battery diagnostics focuses on battery models and diagnosis algorithms for battery state of charge (SOC) and state of health (SOH) estimation. Battery prognostics elaborates data-driven prognosis algorithms for predicting the remaining useful life (RUL) of battery SOC and SOH. Readers will learn not only basics but also very recent research developments on battery diagnostics and prognostics.