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In this review we discuss our recent efforts directed at understanding the dynamics of catalytic networks, and their utility for performing Boolean logic operations. We start by explaining the “recipe” for the design of experimental, peptide‐based, replication networks, and then the approach we take for simulating their kinetics. The studied networks can be manipulated in order to facilitate molecular replication through all 2‐input Boolean logic operations, and furthermore the operational catalytic pathways can be wired together to perform more complex computational modules and network motifs. Beyond just simulations and the basic experiments, we show that while in principle all the gates may be constructed, symmetry and order constraints limit the types of logic that may be practically achieved. Finally, we describe the use of adaptive networks that form logic gates by responding to changes in the environment (pH …