Lithium-ion batteries are playing a key role in the sustainable energy transition. To fully exploit the potential of this technology, a variety of modeling, estimation, and prediction problems need to be addressed to enhance its design and optimize its utilization. Batteries are complex electrochemical systems whose behavior drastically changes as a function of aging, temperature, C-rate, and state of charge, posing unique modeling and control research questions.In this tutorial paper, we provide insights into three battery modeling methodologies, namely first principle, machine learning, and hybrid modeling. Each approach has its own strengths and weaknesses, and by means of three case studies we describe main characteristics and challenges of each of the three methods.