PYMIEDAP (the Python Mie Doubling-Adding Programme) is a Python-based tool for computing the total linearly and circularly polarized fluxes of incident unpolarized sunlight or starlight that is reflected by solar system planets or moons, respectively, or by exoplanets at a range of wavelengths. The radiative transfer computations are based on an doubling-adding Fortran algorithm and fully include polarization for all orders of scattering. The model (exo)planets are described by a model atmosphere composed of a stack of homogeneous layers containing gas and/or aerosol and/or cloud particles bounded below by an isotropically depolarizing surface (that is optionally black). The reflected light can be computed spatially resolved and/or disk-integrated. Spatially resolved signals are mostly representative for observations of solar system planets (or moons), while disk-integrated signals are mostly representative for exoplanet observations. PYMIEDAP is modular and flexible, and allows users to adapt and optimize the code according to their needs. PYMIEDAP keeps options open for connections with external programs and for future additions and extensions. In this paper, we describe the radiative transfer algorithm that PYMIEDAP is based on and the principal functionalities of the code. We also provide benchmark results of PYMIEDAP that can be used for testing its installation and for comparison with other codes.