In a joint work with Claudio Murolo and Andrew du Plessis we proved the smooth Whitney fibering conjecture, in particular for every stratum X of a Whitney stratified set, locally near points of X the foliation defined by the Thom-Mather topological trivialization can be chosen, via suitable vector fields, so that the tangent spaces to the leaves are continuous at X. Moreover the associated wings have a similar property and are Whitney regular. As an application we describe a joint result with Claudio Murolo: every compact Whitney stratified set admits a Whitney cellulation, i.e. a cellulation such that the cells form a Whitney stratification. This resolves a homology problem of Mark Goresky.