This work provides an overview of available methods and algorithms for on-board capacity estimation of lithium-ion batteries. An accurate state estimation for battery management systems in electric vehicles and hybrid electric vehicles is becoming more essential due to the increasing attention paid to safety and lifetime issues. Different approaches for the estimation of State-of-Charge, State-of-Health and State-of-Function are discussed and analyzed by many authors and researchers in the past. On-board estimation of capacity in large lithium-ion battery packs is definitely one of the most crucial challenges of battery monitoring in the aforementioned vehicles. This is mostly due to high dynamic operation and conditions far from those used in laboratory environments as well as the large variation in aging behavior of each cell in the battery pack. Accurate capacity estimation allows an accurate driving range prediction and accurate calculation of a battery's maximum energy storage capability in a vehicle. At the same time it acts as an indicator for battery State-of-Health and Remaining Useful Lifetime estimation. (C) 2015 Elsevier B.V. All rights reserved.