Trapped Rydberg ions are a novel platform for quantum information processing. This approach combines the advanced quantum control of trapped ions and the strong dipolar interaction of Rydberg atoms. In this thesis, a strong dipoledipole interaction has been demonstrated and a sub-microsecond entangling gate has been implemented in a cold two-ion crystal. After minimizing the polarizability of the Rydberg state by microwave dressing and understanding the effect of the quadrupole radio-frequency trap,the entangling gate has been applied in a warm 12-ion crystal.