When the conventional superconductor niobium and the cuprate superconductor YBa2Cu3O7- (YBCO) are connected in a ring-shaped geometry, the ground state is characterized by a spontaneously generated current corresponding to a half-integer magnetic flux quantum in the large inductance limit. The spontaneously generated currents result from a -phase shift originating from the difference in order parameter symmetry for niobium (s-wave) and YBCO (dx2-y2-wave). The fractional magnetic flux quanta in high-Tc/low-Tc superconducting structures have been used for an angle-resolved phase sensitive study to the order parameter symmetry in YBCO, which was found to contain an s-wave admixture of at least 9%. Moreover, the experiments set an upper limit of a few percent on any complex admixture. The fractional flux quanta have also been used for the realization of a novel superconducting logic circuit element: a toggle flip-flop with integrated -rings. The dx2-y2-wave-induced -phase shifts alleviate the need for bias current lines and improve design-, fabrication- and operation margins. The -ring-based toggle flip-flop has been integrated in a test circuit and its correct operation was demonstrated. Besides in -rings, the fractional magnetic flux quanta have also been studied in a so-called corner geometry. The first on-chip manipulation and read-out of half-integer flux quanta in a 0--0 junction is presented. This is an important step forward if corner junctions are to be integrated in superconducting electronics