Connecting theoretical models for exotic quantum states to real materials is a key goal in quantum material synthesis. Among such theoretical models, a “toy model” is one made deliberately simplistic in order to demonstrate new physical concepts and their underlying mechanisms.  We describe here our recent progress in experimentally realizing “toy model” quantum materials which, in analogy to their theoretical counterparts, are designed to capture simple model systems by lattice and superlattice design.  First, we discuss improvements in the realization of the kagome lattice model in materials with reduced inter-kagome-layer coupling, including observation of both the massless and infinitely massive electronic bands expected therein.  Second, we describe recent progress in realizing clean-limit 2D superconductivity in natural superlattice materials, which potentially connect to models for finite-momentum pairing and topological superconducting states. We comment on the perspective for realizing further toy model systems in complex material structures.