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A quantitative and predictive microscopic theoretical framework that can describe reactions induced by α particles (4He nuclei) and heavier projectiles is currently lacking. Such a framework would contribute to reducing uncertainty in the modeling of stellar evolution and nucleosynthesis and provide the basis for achieving a comprehensive understanding of the phenomenon of nuclear clustering (the organization of protons and neutrons into distinct substructures within a nucleus). We have developed an efficient and general configuration-interaction framework for the description of low-energy reactions and clustering in light nuclei. The new formalism takes full advantage of powerful second-quantization techniques, enabling the description of α-α scattering and an exploration of clustering in the exotic 12Be nucleus. We find that the 4He(α,α)4He differential cross section computed with non-locally regulated chiral interactions is in good agreement with experimental data. Our results for 12Be indicate the presence of strongly mixed helium-cluster states consistent with a molecular-like picture surviving far above the 6He+6He threshold, and reveal the strong influence of neutron decay in both the 12Be spectrum and in the 6He(6He,α)8He cross section. We expect that this approach will enable the description of helium burning cross sections and provide insight on how three-nucleon forces influence the emergence of clustering in nuclei.