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Assessing the effects of a policy based on observational data from a different policy is a common problem across several high-stake decision-making domains, and several off-policy evaluation (OPE) techniques have been proposed. However, these methods largely formulate OPE as a problem disassociated from the process used to generate the data (i.e. structural assumptions in the form of a causal graph). We argue that explicitly highlighting this association has important implications on our understanding of the fundamental limits of OPE. First, this implies that current formulation of OPE corresponds to a narrow set of tasks, i.e. a specific causal estimand which is focused on prospective evaluation of policies over populations or sub-populations. Second, we demonstrate how this association motivates natural desiderata to consider a general set of causal estimands, particularly extending the role of OPE for counterfactual off-policy evaluation at the level of individuals of the population. A precise description of the causal estimand highlights which OPE estimands are identifiable from observational data under the stated generative assumptions. For those OPE estimands that are not identifiable, the causal perspective further highlights where more experimental data is necessary, and highlights situations where human expertise can aid identification and estimation. Furthermore, many formalisms of OPE overlook the role of uncertainty entirely in the estimation process.We demonstrate how specifically characterising the causal estimand highlights the different sources of uncertainty and when human expertise can naturally manage this uncertainty. We discuss each of these aspects as actionable desiderata for future OPE research at scale and in-line with practical utility.