The broad conjecture that the critical Ising model in two dimensions is described by a Conformal Field Theory (CFT) has seen a number of rigorous justifications in recent years, notably including Chelkak, Hongler, and Izyurov's recent proof that the correlations between primary fields of the model converge under scaling limit to explicit CFT correlations. We prove an analogous result for the massive model, i.e. convergence of correlations between the spin, disorder, fermion, and energy fields under a near-critical scaling limit setting. The massive model, by definition, is not conformally invariant and therefore its correlations do not enjoy a same kind of explicit description as in the critical case; however, analogues of the critical operator product expansions (OPE's) persist and the correlations may be bosonized and identified with correlations in the massless Sine-Gordon model. Based on joint works with Chelkak, Izyurov, Webb, and others.