  Single electron tunneling into small superconducting islands is sensitive to
the gap energy of the excitations created in the process and, hence, depends on
the electron number parity. At low temperature the properties of the system are
2e-periodic in the applied gate voltage, turning e-periodic at higher
temperature. We evaluate the tunneling rates and determine the probabilities
for the even and odd state as well as the cross-over condition from the balance
between different processes. Our analysis includes excitations in the leads.
They are essential if the leads are superconducting. The influence of parity
effects on single electron tunneling, Cooper pair tunneling, and the Andreev
reflection in superconducting transistors yields rich structures in the I-V
characteristic, which explains recent experimental findings.
