CONCEPT (COsmological N-body CodE in PyThon) simulates cosmological structure formation. It can simulate matter particles evolving under self-gravity in an expanding background. The code offers multiple gravitational solvers and has adaptive time integration built in. In addition to particles, CONCEPT also evolves fluids at various levels of non-linearity, providing the means for the inclusion of more exotic species such as massive neutrinos, as well as for simulations consistent with general relativistic perturbation theory. Various non-standard species, such as decaying cold dark matter, are fully supported. CONCEPT includes a sophisticated initial condition generator and can output snapshots, power spectra, bispectra ,and several kinds of renders.