Scientists can now trap single atoms or photons, prepare these particles in well-defined states and follow their evolution in real time. Localization of ions leads to unique characteristics: extremely narrow atomic lines under weak perturbation by neighbouring particles (the ions are isolated in a vacuum environment) as a consequence of accurate control of quantum states. Trapping and cooling techniques for electrically charged particles expand the frontiers of physics and yield to measurements of unprecedented accuracy. Since the very beginning, experiments with ion traps enable ultrahigh resolution spectroscopy and metrology measurements of fundamental quantities such as the electron and positron g-factors, or the fine structure constant α. Ion traps are intensively used in studies of quantum optics, fundamental tests of quantum physics and general relativity, ultrahigh resolution spectroscopy, Quantum Information Processing (QIP), atomic and nuclear physics. Late results demonstrate that optical clocks based on ultracold trapped atoms and ions exhibit an accuracy that is at least three orders of magnitude better with respect to actual microwave (caesium) clocks used for navigation. In addition, The European Space Agency (ESA) Space Observation programme will benefit from optical clocks embarked on space missions, that open remarkable perspectives for relativistic geodesy and remote atmospheric sensing.