  Quantum pumping in closed systems is considered. We explain that the Kubo
formula contains all the physically relevant ingredients for the calculation of
the pumped charge ($Q$) within the framework of linear response theory. The
relation to the common formulations of adiabatic transport and ``geometric
magnetism" is clarified. We distinguish between adiabatic and dissipative
contributions to $Q$. On the one hand we observe that adiabatic pumping does
not have to be quantized. On the other hand we define circumstances in which
quantized adiabatic pumping holds as an approximation. The deviation from exact
quantization is related to the Thouless conductance. As an application we
discuss the following examples: classical dissipative pumping by conductance
control, classical adiabatic (non dissipative) pumping by translation, and
quantum pumping in the double barrier model. In the latter context we analyze a
3 site lattice Hamiltonian, which represents the simplest pumping device. We
remark on the connection with the popular $S$ matrix formalism which has been
used to calculate pumping in open systems.
