The non-thermal spectra of blazars, observed from radio to GeV/TeV gamma-rays, reveal two pronounced components, both produced by radiation by energetic particles. One peaks in the IR - to soft X-ray band, radiating via the synchrotron process; the other, peaking in the high-energy gamma-rays, is produced by the Compton process. These spectra -- and, in particular, the asca data -- suggest that the origin of the seed photons for Comptonization is diverse. In the High-energy peaked BL Lac objects (HBLs), the dominant seed photons for Comptonization appear to be the synchrotron photons internal to the jet (SSC process). In the quasar-hosted blazars (QHBs), on the other hand, the X-ray band emission is still dominated by the SSC process, while the MeV to GeV range is produced by Comptonization of external photons such as the emission line light. In the context of this three-component model, we derive the magnetic field of 0.1 - 1 Gauss for all classes of blazars. Lorentz factors gamma_{peak} of electrons radiating at each peak of the nuFnu spectra are estimated to be ~10^{5}$ for HBLs; this is much higher than ~10^{3}$ for QHBs. This difference is consistent with the fact that the four sources that are known to emit TeV gamma-rays (TeV blazars) are all classified as HBLs. Among the TeV blazars, Mkn 421 is one of the brightest and most variable emitters from ultraviolet (eV) to hard gamma-ray (TeV) energies.The multi-frequency observations including TeV energy band provide the best opportunity to understand high-energy emission from blazar jets. In this paper, we discuss results of multi-frequency analysis and review the results of intensive campaigns for Mkn 421 from 1994 to 1998
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