Monolayer transition metal dichalcogenides (TMDCs) have recently been proposed as an excitonic platform for advanced optical and electronic functionalities(1-3). However, in spite of intense research efforts, it has not been widely appreciated that TMDCs also possess a high refractive index(4,5). This characteristic opens up the possibility to utilize them to construct resonant nanoantennas based on subwavelength geometrical modes(6,7). Here, we show that nanodisks, fabricated from exfoliated multilayer WS2, support distinct Mie resonances and anapole states(8) that can be tuned in wavelength over the visible and near-infrared range by varying the nanodisk size and aspect ratio. As a proof of concept, we demonstrate a novel regime of light-matter interaction-anapole-exciton polaritons-which we realize within a single WS2 nanodisk. We argue that the TMDC material anisotropy and the presence of excitons enrich traditional nanophotonics approaches based on conventional high-index materials and/or plasmonics.