The last years have seen a revolution in ground-based gamma-ray detectors. We can now detect the spectra of nearby TeV blazars like Mrk 421 and Mrk 501 out to similar to 20 TeV, and during the strongest flares, we can now follow fluctuations in these spectra on timescales close to the shortest ones likely in these objects. We point out that this represents a unique opportunity. Using these and future detectors in combination with broadband X-ray satellites like BeppoSAX and Rossi X-Ray Timing Explorer, we will be able to simultaneously follow all significant X-ray/gamma-ray variations in a blazar's emission. This will provide the most stringent test yet of the synchrotron-Compton emission model for these objects. In preparation for the data to come, we present sample synchrotron self-Compton model calculations using a fully self-consistent, accurate code to illustrate the variability behavior one might see and to show how good timing information can probe physical conditions in the source. If the model works, i.e., if X-ray/TeV variations are consistent with being produced by a common electron distribution, then we show it is possible to robustly estimate the blazar's intrinsic TeV spectrum from its X-ray spectrum. Knowing this spectrum, we can then determine the level of absorption in the observed spectrum. Constraining this absorption, which is due to gamma-ray pair production on diffuse radiation, provides an important constraint on the infrared extragalactic background intensity. Without the intrinsic spectrum, we show that detecting absorption is very difficult and argue that Mrk 421 and Mrk 501, as close as they are, may already be absorbed by a factor 2 at similar to 3 TeV This should not be ignored when fitting emission models to the spectra of these objects.
