Battery management system (BMS) is an integral part of the Lithium-ion battery (LIB) for safe operation and power management. The advanced BMSs also provide state of charge (SOC) and state of health (SOH) information. Accurate estimation of the SOC and SOH from a sparse set of input and output measurements (voltage, current, and surface temperature) is challenging due to the internal inter-related complex electrochemical side reactions. Several factors, such as charge/discharge rate, operating temperature, internal aging, abnormal charging-discharging cycles, and internal faults, adversely affect the LIB's health. To aid the development of intelligent and robust BMS with the capability of health-conscious decision making, a deep understanding of the internal degradation mechanisms and the effect of external degradation-inducing factors are of primary importance. This paper presents an in-depth review of internal and external degradation mechanisms at both anode and cathode of LIB with their corresponding mathematical models and correlation with SOH metrics (capacity and power fade). Different electrochemical models integrated with the internal degradation mechanisms and their governing equations are discussed and summarized. The effects of the external aging factors on capacity and power fade and the dominant degradation mechanism under cycling and stored conditions are also reviewed and tabulated for quick reference. Recent developments in BMS's capabilities for SOH estimation using advanced and intelligent algorithms under various internal degradation conditions are also presented. Finally, the challenges in modeling, estimation of SOH, and several future research directions for developing self-learning and smart BMS are provided.