Recent progress and future prospects of matter-wave interferometry with complex organic molecules and inorganic clusters are reviewed. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. The theoretical concepts underlying these experiments and the experimental challenges are discussed. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter-wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. The prospects for probing the quantum superposition principle are investigated in the limit of high particle mass and complexity.