Book excerpt: Current Earth system models (ESMs) struggle to accurately simulate the spatiotemporal variability of the desert dust cycle and the impact of dust aerosols on Earth's climate and ecosystems. This is in part because these models lack several essential land-surface aeolian processes that couple dust with climate and land-surface changes. We address these fundamental problems and improve the representation of dust emission in ESMs using both a process-based approach and a data-driven approach. First, we develop a new process-based dust emission scheme that couples dust emission better with simulated land-surface processes in ESMs, with improved descriptions of (1) the effect of soil texture on the dust emission threshold, (2) the effects of rocks and vegetation on dissipating the surface wind stress, (3) the effects of boundary-layer turbulence on driving intermittent dust emissions, and (4) a simple methodology to rescale coarser-resolution emission simulations to match the spatial variability of higher-resolution emission simulations in ESMs. We use the revised dust emission scheme to model global dust emissions in a standalone model forced by reanalyzed meteorology and land-surface fields. The resulting simulated emissions show substantially better agreement than other existing emission models against observationally constrained regional dust emissions. Second, we implement the new emission scheme into the Community Earth System Model version 2 (CESM2) for a present-day (2004-2008) dust cycle simulation. The results show that our scheme significantly reduces the CESM2 simulation bias against observations compared to CESM's default emission scheme and improves the correlations against observations of key dust variables such as dust aerosol optical depth (DAOD) and surface particulate matter (PM) concentration. Third, we use a data-driven approach to construct a globally gridded historical (1841-2000) dust emission inventory by empirically combining multiple sedimentary records of dust deposition with observational and modeling constraints on the modern-day dust cycle. The derived inventory contains the interdecadal variability of dust emissions as forced by the rising trends in the observed deposition time series, which show a global emission increase of $\sim$50\% for 1841-2000. We evaluate the inventory's effectiveness in enforcing a historical dust increase in ESMs by using it to force a long-term (1851-2000) dust cycle simulation in CESM2. The simulated dust deposition is in reasonable agreement with the long-term variability in most dust deposition records and with independently measured long-term trends in dust concentrations. This contrasts with dust simulations from the Coupled Model Intercomparison Project (CMIP6), which show little to no secular trends. Our studies thus provide two approaches to advancing the Earth system modeling of desert dust aerosols. The new process-based dust emission scheme enables more accurate simulations of the dust cycle's present-day spatial and day-to-day variability, enhancing short-term weather and air pollution forecasting power on a daily timescale. The empirically derived dust emission inventory allows realistic simulations of the historical dust increase, thereby improving the accuracy of aerosol radiative forcing predictions in climate change assessments across multidecadal timescales. Both approaches will thus improve dust cycle simulations in ESMs across multiple timescales of interest.