Surface pits are commonly formed where threading dislocations emerge from a thin film. Observations of facetted pits are common in complex materials where the Burgers vector tends to be large. Such materials also commonly exhibit hollow-core dislocations/micropipes. In this presentation, we analyze the shapes of surface pits in anisotropic materials. New analytical results will be presented for the isotropic surface energy case that extends the classical analyses. We show that faceting is dominated by surface energy, while the elastic energy associated with the dislocation largely controls the size of the pits. In cases when the temperature is well below the roughening point, the fully faceted Wulff shape will lead to fully faceted pit shape. Analytical predictions for the pit shape and size are made. Application of this method to interpret observations of dislocation pits in GaN and InGaN/GaN superlattices will be presented.