First I recall the construction of the p-adic Deligne--Lusztig stack attached to a (quasi-split) p-adic reductive group G/Q_p. The fibers of this stack over Isoc_G are p-adic DL-spaces which in turn contain parahoric DL-varieties. Their cohomology is a source for interesting (smooth) representations (of parahoric subgroups) of G(Q_p). I will explain two applications to the study of supercuspidal representations: (1) construction of some new supercuspidals, (2) computation, based on a theorem of T. Feng, of Fargues--Scholze parameters of some supercuspidals. There results are based on several joint works with O. Dudas, S. Nie, P. Tan.