Today, atom interferometers are used for a variety of experiments to determine fundamental constants and to investigate fundamental forces, such as demonstrated in the measurement of the photon recoil for the determination of the fine-structure constant, the measurement of the gravitational constant G, as well as gravimeters and gravity-gradiometers or atomic gyroscopes. Tests of the principle of equivalence, the measurement of relativistic effects or the realization of precise inertial references will challenge the full potential of atom interferometry. This lecture reports on our work towards a high-resolution Sagnac atom interferometer for measuring tiny rotations and accelerations. Beside the development and test of new atom-optical methods, future fields of applications of this apparatus are the monitoring of variations of the Earth's rotation rate, as well as the exploration of fundamental physical effects. The set-up is designed as a transportable device which permits comparisons with the largest stationary existing ring laser gyroscopes which are to date one of the most sensitive rotation sensors. The device is based on a dual Mach-Zehnder–type interferometer using laser-cooled rubidium atoms in a differential measurement scheme. Starting from the interferometers basic concepts, the lecture discusses key elements of the interferometer including the atomic sources, the coherent manipulation of atoms and methods for in situ diagnostics for the optimisation and characterisation of the devices. In future, major improvements of experimental tests of relativity and gravity are expected to be achieved in space. Space permits operation of experimental platforms which provide an environment with reduced inertial noise even down to very low Fourier frequencies corresponding to minutes and hours of measurement times. They also allow for an extension of the free fall, which lasts for seconds in drop towers, to months and years. The second part of the lecture presents research directed towards experiments with atom sensors in space. The lecture focuses on atomic interferometers, as proposed for the HYPER mission, which aims to monitor the spatial structure of the Lense-Thirring effect close to the Earth, as well as on the measurement of the gravitational acceleration including tests of the universality of the free fall of matter waves. In space, the duration of the experiments are eventually limited by the temperature of the atoms. Reduction of systematic effects (such as tidal effects) has to be achieved by the perfect control of the atomic wave function. Dilute Bose-Einstein condensates and ultra-cold Fermi gases are in this respect the ideal source for these experiments. Therefore, the last part of the lecture presents the project QUANTUS (Quanten Gase unter Schwerelosigkeit), which aims at a compact, robust and mobile experiment for the creation of a BEC to be operated in the drop tower facility at the ZARM in Bremen. The QUANTUS apparatus serves as a platform for studying the manipulation of dilute quantum gases at lowest energy scales, probing their coherent evolution over seconds and exploring their potential for precision measurements.