I will present the historical idea of motivic cohomology of smooth algebraic variety, in order to motivate a new construction of motivic cohomology that works for general schemes. This new theory generalises the recent construction of Elmanto-Morrow over a field. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A^1-invariant in general, but it recovers classical motivic cohomology on smooth schemes over a field (by the work of Elmanto-Morrow) or over a Dedekind domain (by recent work in progress with Arnab Kundu).