Metal-halide perovskite-based tandem solar cells show great promise for overcoming the Shockley-Queisser single-junction efficiency limit via low-cost tandem structures, but so far they employ conventional bottom-cell materials that require stringent processing conditions. Meanwhile, difficulty in achieving low-bandgap (<1.1 eV) perovskites limits all-perovskite tandem cell development. Here we propose a tandem cell design based on a halide-perovskite top-cell and a chalcogenide colloidal quantum dot (CQD) bottom-cell, where both materials provide bandgap-tunability and solution-processability. Theoretical efficiency of 43% is calculated for a tandem-cell bandgap combination of 1.55 eV (perovskite) and 1.0 eV (CQDs) under 1-sun illumination. We highlight that inter-subcell radiative coupling contributes significantly (>11% absolute gain) to the ultimate efficiency via photon recycling. We report initial experimental demonstration of a solution-processed monolithic perovskite/CQD tandem solar cell, showing evidence for subcell voltage addition. We model that a power-conversion efficiency of 29.7% is possible by combining the state-of-the-art perovskite and CQD solar cells.