Using the Infrared Spectrograph on the Spitzer Space Telescope, we observed the Antennae galaxies obtaining spectral maps of the entire central region and high signal-to-noise 5 − 38µm spectra of the two galactic nuclei and six infrared-luminous regions.The total infrared luminosity of our six IR peaks plus the two nuclei is L IR = 3.8·10 10 L ⊙ , with their derived star formation rates ranging between 0.2 and 2 M ⊙ /yr, with a total of 6.6 M ⊙ /yr. None of the typical mid-infrared tracers of AGN activity is detected in either nucleus of the system, excluding the presence of an dust enshrouded accretion disk. The hardest and most luminous radiation originates from two compact clusters in the southern part of the overlap region, which also have the highest dust temperatures. PAH emission and other tracers of softer radiation are spatially extended throughout and beyond the overlap region, but regions with harder and intenser radiation field show a reduced PAH strength.The strong H 2 emission is rather confined around the nucleus of NGC 4039, where shocks appear to be the dominant excitation mechanism, and the southern part of the overlap region, where it traces the most recent starburst activity. The luminosity ratio between the warm molecular gas (traced by the H 2 lines) and the total far-IR emission is ∼ 1.6 · 10 −4 , similar to that found in many starburst and ULIRGs. The total mass of warm H 2 in the Antennae is 2.5 · 10 7 M ⊙ , with a fraction of warm to total H 2 gas mass of about 0.35%. The average warm H 2 temperature is 302 ± 26 K and appears anti-correlated with the radiation field hardness, possibly due to an evolution of the PDR morphology. The previously reported tight correlation between the H 2 and PAH emission was not found but higher total PAH emission to continuum ratios were found in PDRs with warmer gas.