This article summarizes a series of interconnected researches exploring the potential of applying topological interlocking methodologies to the field of architectural design and fabrication. Specifically, it describes two concurrent approaches to design with interlocking units: the first relying on parametric design logics and mass-customized fabrication processes and the second implementing discrete combinatorial processes for both design and fabrication using modular units. We first outline the historical background of combinatorial thinking in architectural computing and describe the emergence of computational design and digital fabrication. We further present the recent evolution of a combinatorial design paradigm, which challenges the acquired parametric design methodologies in computational architecture research. We then present our research in the field of topological interlocking, focusing on a parametric design approach. We further describe implications of a shift from parametric to combinatorial design logics in architecture. Finally, we present the transition of the topological interlocking research from parametric to combinational logics. In these three sections, we describe design and fabrication methodologies for both approaches and evaluate the potentials and limitations of both. We present recent work in the development of software for combinatorial design within caad software, and its first application is to design topological interlocking systems. We conclude by outlining the future research directions and possibilities of integration between parametric and combinatorial processes in design, fabrication, and assembly of interlocking systems.