A developing Fermi legacy for gamma-ray burst and blazar science is the ability of the LAT to pin down the power-law index of the high energy portion of emission in these sources, and therefore also the index of the underlying non-thermal particle population. This provides, for the first time, clean diagnostics on the shock acceleration environment in the jets/outflows in these extragalactic sources. This paper highlights how such broadband Fermi spectra can be used to probe diffusive acceleration in relativistic, oblique, MHD shocks in bursts and blazars. The key characteristics of relativistic shock acceleration are outlined, in both subluminal and superluminal regimes, including a discussion of an interesting regime of flat distribution generation due to shock drift acceleration that is potentially quite relevant to flat spectrum blazars. Injection efficiencies into the acceleration process are also addressed. Palpable constraints on the frequency of particle scattering and the level of field turbulence, important environmental quantities for relativistic shock studies, are identified using the Fermi observations of GRB 080916c and GRB 090510, and selected energetic blazars such as PKS 2155-304 with TeV-band detections.