Trapped and laser cooled ions provide a robust platform for atomic frequency standards and quantum information architectures. Optical atomic clocks are now the most precise instruments ever realized. They have the potential to discover new physics beyond the standard model, including searches for ultralight scalar dark matter, the time variation of fundamental constants, and violations of Einstein's equivalent principle. The radium ion is a promising high-performance clock candidate, and its clock transitions have the largest positive enhancement factors to potential time variation of the fine structure constant. In this thesis we describe the first laser cooling and trapping of radium ions, measurements of fundamental atomic properties, and the development of a 226Ra+ ion optical clock. We also discuss ongoing efforts towards the realization of 87Sr+ and 225Ra+ ion optical clocks. These species are suited for compact, transportable systems because of their magnetic-field-insensitive clock transitions and easily accessible wavelengths. Finally, we provide plans for work with 87Sr+ and 225Ra+ qubits.