We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.