Ground effects on arc-shaped conformal dielectric resonator antennas (DRAs) working in the TE $^{\mathrm {z}}_{11 \delta }$ mode are investigated and utilized to attain various radiation performances. Manipulation of directivity patterns are achieved with the help of the three-dimensional curved metal ground. The backlobe, beamwidth, broadside gain, backscattering, and cross-polarization level of the antenna are all readily controllable. The geometric theory of diffraction is applied to provide an intuitional explanation for the radiation changes. Detailed analysis is then conducted from the perspective of ground current. It is found that the current distribution is affected by configurations of both the arc DRA and ground plane. Based on this, analytical methods are developed to calculate the ground effects exclusively for conformal arc-shaped DRAs. Next, the design theory of arc DRAs with curved ground is proposed. To demonstrate it, two conformal DRAs owning directional and wide beams, respectively, are designed as paradigms. At last, a prototype is fabricated and measured for validation.