Weakly interacting massive particles (WIMPs) can be gravitationally captured by the Sun and trapped in its core. The annihilation of those WIMPs into Standard Model particles produces a spectrum of neutrinos whose energy distribution is related to the dark matter mass. In this work, we present the theoretical framework for relating an observed neutrino flux to the WIMP-nucleon cross section and summarize a previous solar WIMP search carried out by IceCube. We then outline an ongoing updated solar WIMP search, focusing on improvements over the previous search.