  The description of transport phenomena in devices consisting of arrays of
tunnel junctions, and the experimental confirmation of these predictions is one
of the great successes of mesoscopic physics. The aim of this paper is to give
a self-consistent review of sequential transport processes in such devices,
based on the so-called "orthodox" model. We calculate numerically the
current-voltage (I-V) curves, the conductance versus bias voltage (G-V) curves,
and the associated thermal transport in symmetric and asymmetric two-junction
arrays such as Coulomb-blockade thermometers (CBTs),
superconducting-insulator-normal-insulator-superconducting (SINIS) structures,
and superconducting single-electron transistors (SETs). We investigate the
behavior of these systems at the singularity-matching bias points, the
dependence of microrefrigeration effects on the charging energy of the island,
and the effect of a finite superconducting gap on Coulomb-blockade thermometry.
