The Hall effect was studied in the iron-arsenide-based CaFe_As_, SrFe_As_, BaFe_As_, and Ba(Fe_.__Co_.__)_As_ superconducting compounds in pressures up to 20 kbar in the temperature range of 1.9 to 305 K. These materials form in a tetragonal phase, and they are paramagnetic at ambient temperatures. Upon cooling to__ 150 to 200 K they exhibit a structural phase transformation to orthorhombic, which is accompanied by the onset of antiferromagnetism. This transition is suppressed with the application of pressure, allowing a superconducting phase to develop in a "dome" of pressure values within the temperature-pressure phase diagram. Increasing pressure above 4.9 kbar induces a "collapsed tetragonal" structural phase in CaFe_As_. The coexistence of multiple structural and magnetic phases is consistent with Hall effect data, which demonstrates a convolution of multiple charge carrier types. The complex band structure of these high-temperature superconducting compounds leads to a temperature-dependent Hall coefficient displaying strongly hysteretic values seen in CaFe_As_
