The polarized target of the Spin Muon Collaboration at CERN was used for deep inelastic muon scattering experiments during 1993-1996 with a polarized muon beam to investigate the spin structure of the nucleon. Most of the experiments were carried out with longitudinal target polarization and 190 GeV muons, and some were done with transverse polarization and 100 GeV muons. Protons as well as deuterons were polarized by dynamic nuclear polarization (DNP) in three kinds of solid materials - butanol, ammonia, and deuterated butanol - with maximum degrees of polarization of 94%, 91% and 60%, respectively. Considerable attention was paid to the accuracies of the NMR polarization measurements and their analyses, the accuracies achieved were between 2.0% and 3.2%. The SMC target system with two cells of opposite polarizations, each cell 65 cm long and 5 cm in diameter, constitutes the largest polarized target system ever built and facilitates accurate spin asymmetry measurements. The design considerations, construction and performance of the target are reviewed, (C) 1999 Elsevier Science B.V. All rights reserved.