An understanding of Blue Compact Dwarf galaxies (BCDs) and the processes occurring within their chemically un-evolved environments is fundamental in our understanding of the early universe. This thesis presents an investigation into their physical conditions, kinematics, chemical abundances and dust compositions. An optical integral field spectroscopy investigation of two perturbed BCDs, UM420 and UM462, is presented. Emission line maps show that both galaxies display signs of ongoing perturbation and/or interaction. Electron temperatures, densities and chemical abundances are computed from spectra integrated over the whole galaxies and for each area of star formation. A similar yet more complicated analysis is undertaken of the BCD Mrk996, which displays multi-component emission lines. The high excitation energy [O III] \lambda4363 and [N II] \lambda5755 lines are detected only in the inner regions and purely in broad component form, implying unusual excitation conditions. A separate physical analysis of the broad and narrow emission line regions is undertaken, yielding a revised metallicity and N/O ratio typical for the galaxy's metallicity. The mid-IR properties of 19 BCDs are studied through Spitzer spectral and imaging data. The depeletion of PAH emission in BCDs is investigated and found to be due to formation and destruction effects. The [S III] flux ratio is used as a density diagnostic, showing typically low-densities. Maps of PAH emission and radiation field hardness are derived from IRS spectral mapping data. Blackbody fits to IR photometric SEDs typically reveal two dust components. The observed physical and chemical properties of Mrk 996 are successfully reproduced using the photoionisation code MOCASSIN. The best-fit model involved the inclusion of a filling factor and an amorphous carbon dust component with a two-zone dust distribution. A STARBURST99 input spectrum was used, yielding ages consistent with the known young WR stars and old super star clusters within Mrk 996.