This work demonstrates accurate sculpting of predetermined micron-scale, curved shapes in initially planar solids. Using a 20 keV focused Ga+ ion beam, various features are sputtered including hemispheres, parabolas, and sinusoidal wave forms having dimensions from 1 to 30 μm. Ion sculpting is accomplished by varying the dose at different points within individual scans. The doses calculated per point account for the material-specific, angle-dependent sputter yield, Y(θ), the beam current, and the ion beam spatial distribution. Several target materials are sculpted using this technique. These include semiconductors that are made amorphous or disordered by the high-energy beam and metals that remain crystalline with ion exposure. For several target materials, curved feature shapes closely match desired geometries with milled depths within 5% of intended values. Deposition of sputtered material and reflection of ions from sloped surfaces are important factors in feature depth and profile evolution. Materials that are subject to severe effects of redeposition (e.g., C and Si) require additional dose in certain regions in order to achieve desired geometries. The angle-dependent sputter yields of Si, C, Au, Al, W, SiC, and Al2O3 are reported. This includes normal incidence values, Y(0°), and Yamamura parameters f and Σ.