Psychology is a broad field that endeavors to develop explanatory theories of human capacities and behaviors based on a wide variety of methodologies and dependent measures. Here we argue that whether or not researchers choose to employ modeling (viz., choose to create computational models of their theories over and above their data during the scientific inference process) is one of the most important and divisive factors in our field. Modeling is under- discussed and underemployed, yet, in our view, holds integrative promise for advancing the goals of psychological science. The inherent demands of computational modeling offer invalu- able momentum towards a better, and more open, psychological science. These demands force the scientist to conceptually analyze, specify, and ideally, formalise intuitions and ideas which would otherwise remain implicit or unexamined — something we propose should be called “open theory”. Constraining our inference process through specification and modeling is what will enable us as a field to meaningfully interpret data, and to build theories that explain and predict. In this piece, we present scientific inference in psychology as a path function, where each step shapes the next. Computational modeling can constrain the steps in the path, and has the potential to advance scientific inference over and above the stewardship of the experimental practice (e.g., preregistration, choosing frequentist or Bayesian statistics, power and sample size, and other estimation variables). If as a field we continue to eschew, inadvertently avoid, or remain ignorant of formal and computational modeling, we set ourselves up for a persistent lack of replicability and, moreover, for failure at coherent theory-building that includes explanatory force. We explain how the basic steps in the modeling process can be accomplished and we touch on the cultural and practical issues that need to be faced therein, emphasizing that the advantages of modeling can be achieved by anyone with benefit to all. The process of computational modeling promotes transparent theorising; “open science” should include open theory alongside, e.g., open data and open source code.