  Diffuse radio emission has been detected in a considerable number of galaxy
clusters and groups, revealing the presence of pervasive cosmic magnetic
fields, and of relativistic particles in the large-scale structure (LSS) of the
Universe. Since cluster radio emission is faint and steep spectrum, its
observations are largely limited by the instrument sensitivity and frequency of
observation, leading to a dearth of information, more so for lower-mass
systems. The unprecedented sensitivity of recently commissioned low-frequency
radio telescope arrays, aided by the development of advanced calibration and
imaging techniques, have helped in achieving unparalleled image quality. At the
same time, the development of sophisticated numerical simulations and the
availability of supercomputing facilities have paved the way for
high-resolution numerical modeling of radio emission, and the structure of the
cosmic magnetic fields in LSS, leading to predictions matching the capabilities
of observational facilities. In view of these rapidly-evolving scenerio in
modeling and observations, in this review, we summarise the role of the new
telescope arrays and the development of advanced imaging techniques and discuss
the detections of various kinds of cluster radio sources. In particular, we
discuss observations of the cosmic web in the form of supercluster filaments,
studies of emission in poor clusters and groups of galaxies, and of ultra-steep
spectrum sources. We also review the current theoretical understanding of
various diffuse cluster radio sources and the associated magnetic field and
polarization. As the statistics of detections improve along with our
theoretical understanding, we update the source classification schemes based on
their intrinsic properties. We conclude by summarising the role of the upgraded
GMRT and our expectations from the upcoming Square Kilometre Array (SKA)
observatories.
