Many devices used in the clinical or the cognitive science domain perform electromagnetic measurements, or stimulation, on the human body. To interpret and control bioelectromagnetic phenomena involved with these devices, realistic physiological modeling is required, and accurate numerical solutions of the governing equations must be computed. We present OpenMEEG, which solves the electromagnetic forward problem in the quasistatic regime, for models with piecewise constant conductivity. The core of OpenMEEG resides in the symmetric Boundary Element Method, based on an extended Green Representation theorem. The accuracy of several BEM solutions has been compared for forward electroencephalography, showing that OpenMEEG outperforms the other BEMs. OpenMEEG is an opensource, multiplatform C++ package, with interfaces in Python and Matlab.