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Blazars are among the most extreme astrophysical sources, exhibiting rapid and large-amplitude variability across the entire electromagnetic spectrum, powered by relativistic jets closely aligned with our line of sight. In this talk, I will present a comprehensive view of how broadband temporal and spectral studies can be used to uncover the physical mechanisms operating in blazar jets. Using long-term observations from Fermi-LAT, Swift, and AstroSat, combined with time-resolved X-ray spectral analysis and broadband spectral energy distribution (SED) modeling, I will demonstrate how variability patterns and spectral evolution constrain the underlying radiative processes, and jet physical parameters. I will discuss broadband SED modeling of different flux states in blazars, demonstrating how variations in the particle spectral shape and bulk motion of the emitting region drive the flux evolution. I will briefly discuss how blazar spectral studies can be used to probe extragalactic background light (EBL) attenuation and to identify promising very-high-energy FSRQ candidates for next-generation facilities such as CTA. A major focus of the talk will be on time-resolved X-ray spectral analysis with AstroSat, where I will show how correlations and time delays between spectral parameters provide direct constraints on particle acceleration and cooling timescales, and how spectrally degenerate models can be distinguished using parameter-parameter correlations and pivot energy diagnostics. These studies reveal that, variability is primarily governed by changes in the particle acceleration or escape processes rather than by variations in global jet parameters such as magnetic field or Doppler factor. Finally, I will mention how flux distribution studies of light curves reveal predominantly log-normal behavior, providing simple but powerful evidence for multiplicative processes operating in blazar jets.