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  1. Free, publicly-accessible full text available December 1, 2022
  2. Astrophysical simulations require knowledge of a wide array of reaction rates. For a number of reasons, many of these reaction rates cannot be measured directly and instead are probed with indirect nuclear reactions. We review the current state of the art regarding the techniques used to extract reaction information that is relevant to describe stars, including their explosions and collisions. We focus on the theoretical developments over the last decade that have had an impact on the connection between the laboratory indirect measurement and the astrophysical desired reaction. This review includes three major probes that have been, and will continue to be, widely used in our community: transfer reactions, breakup reactions, and charge-exchange reactions.