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Beta-decay and muon-capture experiments in nuclei are reviewed. The conservedvector current hypothesis is confirmed through the observed constancy of thevector coupling constant determined from the superallowed Fermi transitions andfrom the measurement of the weak-magnetism term in mirror Gamow-Tellertransitions. The axial-vector and pseudoscalar coupling constants in thenucleon are determined from neutron decay and muon capture on the protonrespectively. In finite nuclei, evidence for these coupling constants beingreduced relative to their free-nucleon values is discussed. Meson-exchangecurrents are shown to be an important correction to the time-like part of theaxial current as evident in first-forbidden beta decays. Tests of the StandardModel are discussed, as well as extensions beyond it involving right-handcurrents and scalar interactions.Comment: 67 pages, plain LaTex, uses worldsci.sty, two figures embedded in  manuscript as tex statements. A chapter for a book entitled 'The Nucleus as a  Laboratory for Studying Symmetries and Fundamental Interactions', eds. E.M.  Henley and W.C. Haxto

CURRENTS AND THEIR COUPLINGS IN THE WEAK SECTOR OF THE STANDARD MODEL