We develop a microscopic analysis of superconducting and dissipative currents in junctions between superconductors with d-wave symmetry of the order parameter. We study the proximity effect in such superconductors and show that for certain crystal orientations the superconducting order parameter can be essentially suppressed in the vicinity of a nontransparent specularly reflecting boundary. This effect strongly influences the value and the angular dependence of the dc Josephson current j S. At T∼ T c it leads to a crossover between j S∝ T c-T and j S∝(T c-T) 2 respectively for homogeneous and nonhomogeneous distribution of the order parameter in the vicinity of a tunnel junction. We show that at low temperatures the current-phase relation j S (cphi) for superconductor–normal-metal–superconductor junctions and short weak links between d-wave superconductors is essentially nonharmonic and contains a discontinuity at cphi= 0. This leads to further interesting features of such systems which can be used for pairing symmetry tests in high-temperature superconductors (HTSC). We also investigated the low-temperature I-V curves of normal-metal–superconductor and superconductor-superconductor tunnel junctions and demonstrated that depending on the junction type and crystal orientation these curves show zero-bias anomalies I∝ V 2, I∝ V 2 ln (1/V), and I∝ V 3 caused by the gapless behavior of the order parameter in d-wave superconductors. Many of our results agree well with recent experimental findings for HTSC compounds.