Summary: This paper is concerned with initial-boundary-value problems (IBVPs) for a class of nonlinear Schrödinger equations posed either on a half line \(\mathbb R^+\) or on a bounded interval \((0,L)\) with nonhomogeneous boundary conditions. For any \(s\) with \(0\leq s<5/2\) and \(s\neq 1/2\), it is shown that the relevant IBVPs are locally well-posed if the initial data lie in the \(L^2\)-based Sobolev spaces \(H^s(\mathbb R^+)\) in the case of the half line and in \(H^s(0,L)\) on a bounded interval, provided the boundary data are selected from \(H_{\mathrm{loc}}^{(2s+1)/4}(\mathbb R^+)\) and \(H^{(s+1)/2}_{\mathrm{loc}}(\mathbb R^+)\), respectively. (For \(s>\frac{1}{2}\), compatibility between the initial and boundary conditions is also needed.) Global well-posedness is also discussed when \(s\geq 1\). From the point of view of the well-posedness theory, the results obtained reveal a significant difference between the IBVP posed on \(\mathbb R^+\) and the IBVP posed on \((0,L)\). The former is reminiscent of the theory for the pure initial-value problem (IVP) for these Schrödinger equations posed on the whole line \(\mathbb R\) while the theory on a bounded interval looks more like that of the pure IVP posed on a periodic domain. In particular, the regularity demanded of the boundary data for the IBVP on \(\mathbb R^+\) is consistent with the temporal trace results that obtain for solutions of the pure IVP on \(\mathbb R\), while the slightly higher regularity of boundary data for the IBVP on \((0,L)\) resembles what is found for temporal traces of spatially periodic solutions.