Experimental research at the nanoscale continues to challenge our ability to predict the behavior of quantum systems. Advances with lithographically patterned solid-state electronic devices have enabled multiple platforms for the simulation of quantum matter. In particular, semiconductor quantum dots and superconducting qubits provide tools for studying the wealth of physics induced by nonlinearities at the single electron and single microwave-photon level, respectively, and have been separately pursued as enabling technologies for qubits. In recent years, hybrid devices that combine such historically distinct lines of research have received greater attention, whether to enable novel sensing or measurement applications, or to couple small systems of qubits together at long range (e.g. quantum transduction). I will showcase the rich behaviors and phases of quantum matter that coupled quantum dots can exhibit, including a surprising transport mechanism called cotunneling drag, signatures of Kondo physics with emergent symmetry , and non-Fermi liquid states. I will also discuss my work towards fabricating superconducting qubits on silicon-on-insulator substrates for hybrid device applications. The integration of quantum dots and superconducting resonators promises to yield new probes for studying quantum matter, and superconducting qubits are coming of age in their own right for the implementation of many-body spin models.