Active Galactic Nuclei (AGNs) are extremely powerful objects emitting over a wide range
of wavelengths from radio to gamma-rays. An AGN is a complex system consisting of the
central super-massive black hole, an accretion disk, dusty torus, and clouds of gas
orbiting the black hole, as well as out-flowing matter (which moves away from the central
black hole) in the form of collimated relativistic jets. Two major classes of AGNs that
have been established are radio-loud and radio-quiet. Flat spectrum radio quasars (FSRQs)
and BL Lacerate objects (BL Lacertae) together are coined as blazars, a subset of core
dominated radio-loud AGNs, known to be variable at all accessible time scales over entire
EM spectra. The spectral energy distribution (SED) of blazars display two well-defined
broad spectral components. Blazars are the special laboratories for extreme physics which
we would like to explore.

The analysis presented in this thesis is aimed to provide a more detailed multi-wavelength
understanding of blazars. We have analyzed Optical and Radio observations together with
multi-frequency archival data of blazars in order to study flux-colour variability at diverse
timescales, possible quasi-periodic oscillations (QPOs), correlated variability, multi-band
SEDs, spectral Indices variations and core shift effect. We have developed statistical
techniques and the analysis methodology to extract the maximum possible information from an
observed blazar light curve.

We have carried out quasi-simultaneous and relatively dense temporal observations of four
blazars (2 BL Lacertae and 2 FSRQs) during the observing season 2012 − 2016. This is extensive
study of these blazars on all timescales. Also, we searched for the colour variations on
intraday and short timescales but significant colour variation was observed only on few
instances for these targets which can be attributed to the models involving shock propagating
down the jets. We searched for possible correlations between colour and magnitude and obtain
that all blazars followed the bluer-when-brighter trend which can be explained by the shock-in-jet
models. From the intraday LCs, we inferred the variations to be simultaneous in both the filters
which was confirmed by Discrete correlation function (DCF) analysis technique. Optical QPOs
were found in blazars on intra-day timescales and can be explained by the fluctuations induced
by the disk. Assuming the possible weak QPOs in the blazars are real and are associated with
the innermost portions of their accretion disk, we estimated their central black hole masses.

We presented first detailed investigation of the core shifts with frequency, along with estimation
of jet physical parameters in the case of our source sample, observed using single dish observations
at five radio frequency bands. We have calculated and explained the parameters that can be derived
from the analysis of the radio light curves, including the magnetic field strength and size of the
emitting core, based on physical models proposed in earlier literature.