Gamma-ray bursts are powerful astronomical transient events emitting enormous energy in $\gamma$-rays within a short period. They provide a unique laboratory to those who study them, from relativistic effects such as beaming, jets, shocks, and blastwaves to radiation mechanisms such as synchrotron radiation to galactic and stellar populations. GRBs can be traditionally classified into two sub-groups: Short/hard and long/soft. There are two distinct phases of the GRBs: 1. The prompt emission (emitting mainly in $\gamma$-rays, sometimes in X-ray and optical), which arises because of the internal shocks within the jet, and 2. the afterglow emission (emission from X-ray to radio) happens due to the interaction between the jet and the ambient medium. As GRBs are multi-wavelength phenomena, it is mandatory to follow up using several space and ground-based telescopes. The panchromatic data and extensive modeling provide insight into the radiation mechanisms and the progenitor and environment properties. This thesis tries to bring up different aspects of GRB emissions.

So far, the progenitors of short GRBs have proved elusive. The merger of two neutron stars can produce a rapidly rotating and highly magnetized millisecond magnetar. A significant proportion of the rotational energy deposited to the emerging ejecta can produce a late-time radio brightening from its interaction with the ambient medium. Detection of this late-time radio emission from short GRBs can have profound implications for understanding the physics of the progenitor. We report the radio observations of five short GRBs - 050709, 061210, 100625A, 140903A, and 160821B using the Giant Metrewave Radio Telescope (GMRT) at 1250, 610, and 325 MHz frequencies after $\sim$ $2 - 11$ years from the time of the burst. We find no evidence for such an emission. Despite the non-detection, our study underscores the power of radio observations in the search for magnetar signatures associated with short GRBs. In the second chapter, we present a detailed multi-wavelength analysis of GRB 200524A, which is one of the brightest GRB detected by \textit{Fermi} Gamma Ray Burst Monitor (GBM). An in-depth study of this GRB in the prompt and afterglow phase reveals several exciting features. At a redshift of z $\sim$ 1.256, GRB 200524A is one of the energetic bursts ($E_{\rm iso}$ = $3\times 10^{53}$ erg) which occurred in a medium with a very low ambient density ($3.5\times10^{-3} cm^{-3}$). Finally, we started a comprehensive long-time GRB radio afterglow monitoring of GRB 171205A up to 1500 days since the burst. This is the most extended afterglow detection till now in the history of GRBs. The afterglow evolution of GRB 171205A is enigmatic, and we can clearly state that a standard fireball model fails to explain the radio/mm data. Several power-law components are required to present the complete evolution of the GRB.

In this pre-thesis submission talk, I will cover different aspects of GRB emission, progenitor, and the environment. I will also highlight the importance of future-generation sensitive radio telescopes to detect such emissions and will be able to answer some of the critical issues related to afterglow calorimetry.