<p>A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids within the finite volume framework. In smooth regions, compact least-squares schemes based on interfacial differences of derivatives are utilized to maintain high resolution of multiscale structures, whereas in discontinuous regions, central weighted essentially non-oscillatory schemes are included to enable the oscillation-free shock-capturing capability of the hybrid schemes. Free parameters in the proposed compact least-squares schemes are first optimized to reach a broad range of resolved bandwidths with different levels of dissipation. In addition, a shock detector proposed in our previous work is introduced and validated; it can detect smooth first-order extrema and robustly identify discontinuities. Through the solution of block tridiagonal reconstruction linear systems, the resulting schemes can give an explicit polynomial for each control volume and are efficient with an acceptable computational overhead when compared to the central weighted essentially non-oscillatory schemes. Eventually, benchmarks including one-dimensional and two-dimensional, linear and nonlinear, inviscid and viscous problems on uniform and nonuniform curvilinear grids demonstrate the proposed schemes’ promising applicability in compressible flows that have both multiscale structures and discontinuities.</p>