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 (amp;lt;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. A theoretical efficiency of 43% is calculated for tandem-cell bandgap combinations of 1.55 (perovskite) and 1.0 eV (CQDs) under 1-sun illumination. We highlight that intersubcell radiative coupling contributes significantly (amp;gt;11% absolute gain) to the ultimate efficiency via photon recycling. We report an 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 state-of-the-art perovskite and CQD solar cells.