MBSlib is an efficient and modular multibody systems library for kinematics and dynamics simulation, optimization and sensitivity analysis. The library provides an intuitive modeling interface, modular software architecture, efficient computational algorithms as well as the computation of derivatives with respect to system states, control variables or model parameters. In combination with gradient-based optimization methods, the derivatives can be used to facilitate the numerical solution of optimization problems significantly. The library is free and open. These features make MBSlib a powerful, flexible and lightweight modeling, simulation and optimization library for many technical and biomechanical application.