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The review chapter starts by a pedagogical introduction to the generalconcept of the scattering theory: from the fundamental wave-function picture tothe second-quantization language, with the aim to clear possible ambiguity inconventional textbooks. Recent progress in applying the method to currentfluctuations and oscillating-parameter driven quantum pumping processes ispresented with inclusion of contributions by B\"{u}ttiker, Brouwer, Moskalets,Zhu, etc. In particular, the spin-orbit-coupling affected shot noise can bedealt with by taking into account the spin-dependent scattering processes. Alarge shot noise suppression with the Fano factor below 0.5 observedexperimentally can be illustrated by effective repulsion between electrons withantiparallel spin induced by the Dresselhaus spin-orbit coupling effect. AFloquet scattering theory for quantum-mechanical pumping in mesoscopicconductors is developed by Moskalets et al., which gives a general picture ofquantum pumping phenomenon, from adiabatic to non-adiabatic and from weakpumping to strong pumping.

Development in the Scattering Matrix Theory: From Spin-Orbit-Coupling Affected Shot Noise to Quantum Pumping