Many questions related to the physics of jets of Active Galactic Nuclei remain open. A particular subclass of AGN, blazars, have a jet pointing towards the Earth. Such suitable orientation of the jet allows us to probe a rich variety of poorly understood physical phenomena related to relativistic outflows. Blazars show non-thermal emission, originating from the jet, which is highly variable across the entire electromagnetic spectrum, from radio frequencies to TeV gamma-rays. The energy flux can enhance by an order of magnitude on time-scales as short as minutes, a phenomenon referred to as a “flare”, and as long as months or even years. Despite the growing amount of available multi-wavelength (MWL) data, the origin and the physical mechanisms behind the frequently observed flaring events in blazars are still not well understood. Many attempts have been made to describe the flares with different emission models, but detailed properties of flux variation patterns (light curves) in different wavebands remain difficult to reproduce. In order to identify physical processes that are involved during blazar outbursts, I have developed a versatile radiative code, based on a time-dependent treatment of particle acceleration, escape and radiative cooling. The code computes time evolution of the distribution function of electrons in the blazar emitting zone and the spectrum of the Synchrotron Self-Compton (SSC) emission by these electrons. I applied the code to a giant MWL flare of the blazar Mrk 421, a representative of the BL Lacertae class, which is the brightest VHE flare ever detected from this source. In our approach, we consider the flare as a moderate perturbation of the quiescent state and search for interpretations with a minimum number of free parameters. As a result, I developed a novel physical scenario of the flaring activity that describes the data set, comprising spectra in the high state of the source in different energy ranges, and MWL light curves from the optical domain to the VHE gamma-ray band. In this scenario, the process initiating the outburst is the second-order Fermi acceleration of particles due to turbulence arising in the vicinity of the blazar stationary emission region. In this thesis, I also performed analysis of High Energy Stereoscopic System (H.E.S.S.) data of two giant flares of the blazar 3C 279, a representative of the Flat Spectrum Radio Quasars (FSRQ) class. Finally, I contributed to preparation of Cherenkov Telescope Array (CTA), which is a new-generation ground-based gamma-ray observatory, expected to start operations in 2022. The instrument, which is presently under development, will have greatly improved performance compared to currently operating Imaging Atmospheric Cherenkov Telescopes (IACTs), including unprecedented spectral coverage from a few tens of GeV to ~300 TeV. In the context of CTA, I performed simulations of the optical performance of the Gamma-Ray Cherenkov Telescope (GCT), one of the three proposed designs of Small-Size Telescopes (SST) for CTA. Also, using the observations of bright stars done by the telescope prototype installed on the site of Paris Observatory in Meudon, I studied the effect of micro-roughness of the telescope mirrors on the point spread function (PSF) and calculated the level of the mirror polishing quality required to optimize the performances.