Noncommutative or free probability is a branch of mathematics that is useful for describing the large-$N$ limits of many $N \times N$ random matrix models. In this theory, classical probability spaces are replaced by pairs $(\mathcal{A},\tau)$, where $\mathcal{A}$ is an (operator) algebra and $\tau \colon \mathcal{A} \to \mathbb{C}$ is a certain kind of linear functional. In such a pair, $\mathcal{A}$ and $\tau$ are conceptualized as the space of ``noncommutative random variables'' and the ``expectation'' functional on $\mathcal{A}$, respectively. The analogy with classical probability goes much further. Indeed, there are notions of distribution, independence, $L^p$ spaces, conditional expectation, and more. My talk will focus on my joint work with David Jekel and Todd Kemp on developing a general noncommutative theory of stochastic calculus and SDEs.