We investigate the tectonics of the South Shetland Trench and Bransfield Strait by performing a detailed study of local seismicity. During 1997--1999 we deployed seven land seismometers and 14 ocean bottom seismometers in the South Shetland Island region. The data we obtained indicate a high level of local seismicity (mb 2--5), and we accurately located ~150 earthquakes. Many of the earthquakes occur at locations and depths indicative of ongoing subduction in the South Shetland trench. A focal mechanism for the largest event in the forearc indicates shallow angle thrusting. The maximum depth of seismicity is ~65 km, but the majority of the events are shallower than 30 km. These seismic results are consistent with recent magnetic, GPS, and multichannel seismic reflection data that suggest continued subduction at a very slow rate. The South Shetland trench thus represents an extreme end-member of hot subduction resulting from slow convergence of young lithosphere, and the absence of intermediate depth earthquakes is consistent with thermal assimilation of the slab at shallow depths. We have located many earthquakes associated with volcanism and rifting in Bransfield Strait. A swarm of events near a submarine volcano suggests current magmatic activity. A normal faulting focal mechanism in the northeastern part of the strait gives evidence of extension. Earthquakes associated with rifting in the northeastern portion of the strait are clustered along well-established rifts, but the seismicity is much more diffuse to the southwest. This observation is consistent with other evidence that extension has propagated from northeast to southwest.