The heart of this thesis is the multiwavelength (MWL) study of a special subclass of active galactic nuclei (AGN) called blazars. These objects host a supermassive black hole as their central engine. They present a relativistically boosted jet that points towards the Earth, acting as a natural particle accelerator, emitting over the entire electromagnetic spectrum, from radio to gamma-ray wavelengths, thus becoming the perfect laboratory for studying the most extreme physics in the Universe. A key signature of blazars is their strong and unpredictable variability, that can lead to enhanced emission states with flux increases of several orders of magnitude. This variability can happen on many different timescales and is also associated with changes in their spectra, as well as different properties that can help reveal the physics underlying the emission of blazars.

We present an analysis of the variability of blazars from a MWL perspective, from radio to gamma rays with data from several instruments and facilities (for instance OVRO in radio, the Steward Observatory and WEBT-GASP in optical, and Fermi-LAT and MAGIC in gamma rays). With these data we construct MWL light curves representing the long-term emission of each blazar and its evolution over time. In particular, we search for interesting patterns in their long-term MWL emission such as periodicities. Variability in blazars is usually interpreted through stochastic processes. The detection of such patterns can therefore be of great interest for unveiling the mechanisms leading to the observed variability.

Moreover, the variability displayed by blazars is also reflected in changes in their optical spectrum. This spectrum is generally dominated by the non-thermal emission of the relativistic jet. However, other components, such as the stellar emission from the host galaxy, the broad line region and the accretion disc may contribute significantly to this emission. Disentangling the different contributions to the optical emission of these sources is challenging owing to the high dominance of the jet, but is crucial for studying and understanding the variability detected in blazars. For this reason, we also propose a variability study of the spectra of blazars by applying a statistical technique that enables us to model and reconstruct the observed variability with a reduced number of components that can be related to the physical parts of the blazar, thus decomposing its optical emission in terms of these contributions.

The non-thermal emission of these jets is also characterized by polarized emission due to the presence of strong magnetic fields. Studying this polarization is one of the most useful ways of understanding the nature of magnetic fields in astrophysical jets and in the extreme Universe. Programmes such as RoboPol have started systematical studies of the polarization of blazars with the aim of comprehending the nature of magnetic fields in blazars and their role in the particle acceleration taking place in the jet. However, more studies are still crucial to reach an understanding of the behaviour of these fields. Hence, we have developed a detailed study of 10 years of spectropolarimetric data, characterizing its variability, evolution and properties for a sample of blazars.

In the last years, the development of gamma-ray and multimessenger astronomy has also increased the interest in MWL studies of blazars. These objects dominate the extragalactic gamma-ray sky, being one of the few sources able to accelerate particles up to TeV energies. Therefore, gamma-ray astronomy has also emerged as a hot topic in the last decades when studying these objects. These studies are possible thanks to the current space-based telescopes with satellites and instruments like Fermi-LAT, and ground-based facilities with the current generation of Cherenkov telescopes (MAGIC, HESS and VERITAS). These instruments give access to the most energetic bands of the electromagnetic spectrum and permit a more complete understanding of the broadband emission of blazars. In this context, we have performed an extensive long-term MWL study of the blazar 1ES 0647+250, which has been observed and detected by the MAGIC telescopes during its low emission state between 2009 and 2011, as well as during several flaring events in 2014, 2019 and 2020. Making use of MWL data from radio to gamma rays, we have studied its MWL variability and interband correlations. We have also characterized its spectrum and constructed its spectral energy distribution (SED). With this SED we are able to model and interpret the broadband emission of the source within different theoretical scenarios.