This PhD thesis describes the search for, and analysis of, substructure in the phase-space distribution of stars within 1-2 kpc of the Sun. Such substructure, caused by stellar streams, is an important diagnostic of stellar dynamics and hierarchical formation of the Galaxy. While possibly phase-mixed, stellar streams remain detectable as coherent features in the space of integrals of motion. This thesis describes the development of new search techniques in phase- and [Fe/H]-space to derive "effective" integrals of motion that are most suitable for a comparison with the observables. An application of these techniques to two new data sets which contain radial velocity- and proper motion estimates reveals significant "phase-space overdensities" of stars on similar orbits, of which some are already known, but at least five are described here for the first time. This thesis also outlines a preperatory study in the context of GAIA to measure the local gravitational potential on kpc scale.