Abstract The properties of Josephson junctions of d-wave superconductors, characterized by unusual, non-sinusoidal current-phase relationship (CPR) have been actively investigated in recent years. Less attention has been paid to collective effects arising in systems composed of several d-wave junctions. Extension of the analysis to d-wave junctions reveal some interesting features, such as anomalous periodicity of critical current, and the appearance of frustration effects in junction arrays even in zero external magnetic fields. In this context, we investigate the properties of multi-junction superconducting quantum interferometers composed of d-wave junctions: the possible appearance of additional system phase states, the dynamical behavior and energy relationships of the system and compare these results with those relating to the systems involving s-wave junctions, characterized by sinusoidal CPR. A crucial step in the analysis is accounting for the orientation of the superconducting crystallites with respect to the interfaces. Switching between the phase states of multiple grain boundary junction systems with random grain orientation can result in additional 1/ f noise in granular high- T c superconductors.