This thesis explores the use of highly-charged ions in a range of applications. A special class of highly-charged ions with level crossings, and hence optical transitions between shells, is proposed as the basis for a new generation of optical atomic clocks with exceptional accuracy. Level crossings occur when the energy ordering of electron orbitals changes due to a difference in the number of electrons or protons, reflecting the transition of an atomic system from the neutral atom ordering to

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... the ordering in the Coulomb degenerate limit. Analytical estimates are performed for the systematic effects in such a clock, revealing that the size of systematics can be up to a hundred times smaller than in clocks based on near-neutral ions due to the smaller size of highly-charged ions. A simple method is developed for rescaling the size of known parameters in neutral atoms and near-neutral ions to the regime of high ion charge. High precision atomic calculations are then used to compute various properties of these ions. These include the transition rates and life-times of states, and the sensitivities of energy levels to the variation of fundamental constants. The sensitivity of highly-charged ions to changes in the dimensionless fine-structure constant α = e2/ħc (the q-value ), is found to be greatly enhanced. This is mainly due to the larger ionization energy and high charge found in such ions. We detail the calculations performed for selected highly-charged ion species that may be used in terrestrial searches for evidence of the variation of fundamental constants. Finally, we extend our analysis using available data for highly-charged ions found in astronomical systems. In combination with our ab initio calculations of the sensitivity to α-variation, statistical analysis is applied in order to place limits on the variation of fundamental constants in a white dwarf star, which is representative of the limit of a strong gravitational potential. We also show how the isotopic abundances of such systems can be extracted [...]