Diffuse radio emission from galaxy clusters in the form of radio halos and relics are tracers of the shocks and turbulence in the intra-cluster medium. The imprints of the physical processes that govern their origin and evolution can be found in their radio morphologies and spectra. The role of mildly relativistic population of electrons may be crucial for the acceleration mechanisms to work efficiently. Low frequency observations with telescopes that allow imaging of extended sources over a broad range of low frequencies ($< 2$ GHz) offer the best tools to study these sources. I will review the Giant Metrewave Radio Telescope (GMRT) observations in the past few years that have led to: i) statistical studies of large samples of galaxy clusters, ii) opening of the discovery space in low mass clusters and iii) tracing the spectra of seed relativistic electrons using the Upgraded GMRT.
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