The cdh topology, introduced by Suslin and Voevodsky in the 90's, is a Grothendieck topology on schemes, finite type over an arbitrary field k. Assuming resolution of singularities on k, every such scheme is "locally smooth." I will report on joint with Tom Bachmann and Matthew Morrow on how to make efficient use of the cdh topology, without assuming resolution of singularities, to analyze algebraic K-theory and algebraic cycles of non-smooth schemes (even in mixed characteristic situations). No knowledge of (higher) K-theory and motivic cohomology will be assumed.