The RE (rare earth) Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (REBCO)-coated conductor has shown its high potential in various applications. However, the quench problem under overcurrent conditions, as well as some other problems, is still hindering its practical use. In this research, we have developed a versatile 3D electromagnetic and thermal field coupled FEM analysis tool for REBCO coils, and verified its capability in studying the transient electromagnetic and thermal behaviors, such as current density, Joule heating, temperature distribution, etc., with two case studies. In the first case study, the transient electromagnetic and thermal behaviors of SFCL REBCO coils under overcurrent are studied in the cases of uniform J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> distribution and local J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> degradation. The influence of current leads and local J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</sub> degradation on the quench is investigated. In the second case study, the influence of external energy input, input area, and different time constants of current decrease on the quench of magnet REBCO coils is studied. Moreover, the limitation and improvement of the quench detection scheme based on voltage detection are discussed. The influence of external energy input on the current density distribution is also investigated.