Intense heat fluxes from the divertor incident on material surfaces represent a “bottleneck” problem for the next generation of tokamaks. Advanced divertors, such as the X-Divertor (XD) and Super X-Divertor (SXD), offer a magnetic solution to the heat flux problem by (a) increasing the plasma-wetted area via flux expansion at the targets, and (b) possibly opening regimes of stable, detached operation of the divertor via flux tube flaring, as quantified by the Divertor Index. The benefits of the XD and SXD are derived from their unique magnetic geometries, foregoing the need for excessive gas puffing or impurity injection to mitigate divertor heat fluxes. Using the CORSICA magnetic equilibrium code, XDs and SXDs appear feasible on current- and next-generation tokamaks, with no required changes to the tokamak hardware, and respecting coil conductor limits. Divertor heat and particle transport modeling is performed in SOLPS 5.1 for XD or SXD designs in NSTX-Upgrade, Alcator C-Mod, and CFNS/FNSF. Incident heat fluxes at the targets are kept well below 10 MW/m², even for narrow SOL widths in high-power scenarios. In C-Mod and CFNS, parallel temperature profiles imply the arrestment of the detachment front near the targets. Finally, an X-Divertor for ITER is presented. / text