Coherent passage of Cooper pairs in a Josephson junction (JJ) above the liquid nitrogen temperature has been the first impressive revolutionary effect induced by high critical temperature superconductors (HTS) in the domain of the study of Josephson effect (JE). But this has been only the start. A d-wave order parameter has lead to significant novel insights in the physics of the JE turning into a device the notion of a pi-junction. Spontaneous currents in a frustrated geometry, Andreev bound states, long-range proximity effect have rapidly become standard terms in the study of the JE, standing as a reference bench for conventional systems based on low critical temperature superconductors (LTS) and inspiring analogies for junctions based on novel superconductors discovered in the meantime. The extreme richness of the physics of HTS JJs has not been adequately supported by the expected impact in the applications, the main reason lying in the complexity of these materials and in the consequent unsatisfactory yield and reproducibility of the performances of the JJs within the required limits. The continuous progress in material science, and specifically in the realization of oxide multi-layers, and in nanotechnologies applied to superconductors, accompanied by the advances in a better understanding of the properties of HTS and of HTS devices, has as a matter of fact opened possible novel scenarios and interest in the field. We intend to give a brief overview on interesting new problems concerning HTS JJs of inspiration also for other systems. We also review some ideas and experimental techniques on macroscopic quantum decay phenomena occurring in Josephson structures. The attention is mainly addressed to intermediate levels of dissipation, which characterize a large majority of low critical current Josephson devices and are therefore an unavoidable consequence of nanotechnology applied more and more to Josephson devices.