When conducting shape optimization or aerodynamic design studies, one key step in the design process is the choice of a geometry parametrization method. A parametrization framework using a series of joined Bézier curves is proposed. This framework creates airfoil geometries satisfying point, slope, and curvature continuity across their entire domains. "Anchor" points, or points in two-dimensional, Cartesian space where the airfoil curves are required to pass through and at which the continuity constraints are enforced, can be added to the airfoils to facilitate the imposition of additional, configuration-specific constraints. Example cases of the framework are presented, including a very basic case of an airfoil comprised of two Bézier curves with order ≥ 4, a high-lift multi-element airfoil system, and a highly complex propulsion-airframe-integrated airfoil system. A Python implementation of the framework, pyairpar, is publicly available on the PyPi repository∗ .