We present low- and high-resolution Spitzer /IRS spectra , supplemented by IRAC and MIPS measurements , of 22 blue compact dwarf ( BCD ) galaxies . The BCD sample spans a wide range in oxygen abundance [ 12 + log ( O/H ) between 7.4 and 8.3 ] , and hardness of the interstellar radiation field ( ISRF ) . The IRS spectra provide us with a rich set of diagnostics to probe the physics of star and dust formation in very low-metallicity environments . We find that metal-poor BCDs have harder ionizing radiation than metal-rich galaxies : [ O iv ] emission is \buildrel > \over { \sim } 4 times as common as [ Fe ii ] emission . They also have a more intense ISRF , as indicated by the 71 to 160 µm luminosity ratio . Two-thirds of the sample ( 15 BCDs ) show PAH features , although the fraction of PAH emission normalized to the total infrared ( IR ) luminosity is considerably smaller in metal-poor BCDs ( \sim 0.5 % ) than in metal-rich star-forming galaxies ( \sim 10 % ) . We find several lines of evidence for a deficit of small PAH carriers at low metallicity , and attribute this to destruction by a hard , intense ISRF , only indirectly linked to metal abundance . Our IRS spectra reveal a variety of H _ { 2 } rotational lines , and more than a third of the objects in our sample ( 8 BCDs ) have \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 3 \sigma detections in one or more of the four lowest-order transitions . The warm gas masses in the BCDs range from 10 ^ { 3 } to 10 ^ { 8 } M _ { \odot } , and can be comparable to the neutral hydrogen gas mass ; relative to their total IR luminosities , some BCDs contain more H _ { 2 } than SINGS galaxies .