QuTiP is open-source software for simulating the dynamics of closed and open quantum systems. The QuTiP library depends on the excellent Numpy, Scipy, and Cython numerical packages. In addition, graphical output is provided by Matplotlib. QuTiP aims to provide user-friendly and efficient numerical simulations of a wide variety of quantum mechanical problems, including those with Hamiltonians and/or collapse operators with arbitrary time-dependence, commonly found in a wide range of physics applications. QuTiP is freely available for use and/or modification on all common platforms. Being free of any licensing fees, QuTiP is ideal for exploring quantum mechanics in research as well as in the classroom.