While it is well established that host heterogeneity in transmission and host heterogeneity in susceptibility each individually impact disease dynamics in characteristic ways, it is generally unknown how disease dynamics are impacted when both types of heterogeneity are simultaneously present. Here we explore this question. We first conducted a systematic review of published studies from which we determined that the effects of correlations have been drastically understudied. We then filled in the knowledge gaps by developing and analyzing a stochastic, individual-based SIR model that includes both heterogeneity in transmission and susceptibility and flexibly allows for positive, negative, or zero correlations between transmissibility and susceptibility. We found that in comparison to the uncorrelated case, positive correlations result in major epidemics that are larger, faster, and more likely, whereas negative correlations result in major epidemics that are smaller and less likely. We additionally found that, counter to the conventional wisdom that heterogeneity in susceptibility always reduces outbreak size, heterogeneity in susceptibility can lead to major epidemics that are larger and more likely than the homogeneous case when correlations between transmissibility and susceptibility are positive, but this effect only arises at small to moderate R. Moreover, positive correlations can frequently lead to major epidemics even with subcritical R. To illustrate the potential importance of heterogeneity and correlations, we developed an SEIR model to describe mpox disease dynamics in New York City, demonstrating that the dynamics of a 2022 outbreak can be reasonably well explained by the presence of positive correlations between susceptibility and transmissibility. Ultimately, we show that correlations between transmissibility and susceptibility profoundly impact disease dynamics.