An assessment of the fifth Coupled Models Intercomparison Project (CMIP5) models' simulation of the near-surface westerly wind jet position and strength over the Atlantic, Indian and Pacific sectors of the Southern Ocean is presented. Compared with reanalysis climatologies there is an equatorward bias of 3.3° (inter-model standard deviation of ± 1.9°) in the ensemble mean position of the zonal mean jet. The ensemble mean strength is biased slightly too weak, with the largest biases over the Pacific sector (−1.4 ± 1.2 m/s, −19%). An analysis of atmosphere-only (AMIP) experiments indicates that 28% of the zonal mean position bias comes from coupling of the ocean/ice models to the atmosphere. The response to future emissions scenarios (RCP4.5 and RCP8.5) is characterized by two phases: (i) the period of most rapid ozone recovery (2000–2049) during which there is insignificant change in summer; and (ii) the period 2050–2098 during which RCP4.5 simulations show no significant change but RCP8.5 simulations show poleward shifts (0.33, 0.18 and 0.27°/decade over the Atlantic, Indian and Pacific sectors, respectively), and increases in strength (0.07, 0.08 and 0.15 m/s/decade, respectively). The models with larger equatorward position biases generally show larger poleward shifts (i.e. state dependence). This inter-model relationship is strongest over the Pacific sector (r = −0.91) and weakest over the Atlantic sector (r = −0.39). An assessment of jet structure shows that over the Atlantic sector jet shift is not clearly linked to indices of jet structure whereas over the Pacific sector the distance between the sub-polar and sub-tropical westerly jets appears to be important.