The merger of binaries consisting of a white dwarf (WD) and a neutron star (NS), though much less studied than their NS-NS/WD-WD brethren, are relatively common astrophysical events which may contribute to the transient sky. I will review the background and motivation for studying WD-NS mergers. Dependent on the WD-to-NS mass ratio, mass transfer at Roche-lobe contact may become unstable, and the disrupted WD will be sheared into a hot-dense accretion torus surrounding the NS. I will present recent work modeling these accretion flows on both short (~min) and long (~kyr) timescales. Nuclear burning in the early hyper-Eddington accreting flow fuses matter up the alpha-chain, heating the geometrically thick disk to a marginally bound state prone to outflows. These outflows may power a rapidly-evolving (~week-long) optical transient, broadly consistent with the class of `Ca-rich gap transients’. Finally, by modeling the long-term disk evolution, I show that a WD-NS merger provides a natural mechanism for creating carbonaceous ("diamond") planets orbiting the millisecond pulsar PSR B1257+12, providing new insight into the unusually high proper motion of the pulsar-planet system.