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 of the Universe. Since the radio emission in galaxy systems is faint and its spectrum is steep, itsobservations are largely limited by the instrument sensitivity and frequency of observation, leading to a dearth of information, more so for lower-mass systems. The recent commissioning or upgrade of several large radio telescope arrays, particularly at the low frequency bands (<GHz) is, therefore, a significant step forward. The unprecedented sensitivity of these new instruments, aided by the development of advanced calibration and imaging techniques, have helped in achieving unparalleled image quality and revolutionised the study of cluster-scale radio emission. At the same time, the development of state-of-the-art numerical simulations and the availability of supercomputing facilities have paved the way for high-resolution numerical modelling of radio emission, and the structure of the cosmic magnetic fields, associated with large-scale structures inthe Universe, leading to predictions matching the capabilities of observational facilities. In view of these rapidly-evolving developments in modeling and observations, in this review, we summarise the role of new telescopearrays and the development of advanced imaging techniques and discuss the range of detections of various kinds of cluster radio sources, both in dedicated surveys as well as in numerous individual studies. We pay specific attention to the kinds of diffuse radio structures that have been able to reveal the underlying physics in recent observations. In particular, we discuss observations of large-scale sections of the cosmic web in the form of supercluster filaments, and studies of emission in low-mass systems, such as poor clusters and groups ofgalaxies, and of ultra-steep spectrum sources, the last two being notably aided by low-frequency observations and high sensitivity of the instruments being developed. We also discuss and review the current theoreticalunderstanding of various diffuse radio sources in clusters and the associated magnetic field and polarisation in view of the current observations and simulations. As the statistics of detections improve along with our theoretical understanding, we update the source classification schemes based on the intrinsic properties of these sources. We conclude by summarising the role of the upgraded GMRT (uGMRT) and our expectations from the upcoming Square Kilometre Array (SKA) observatories.