This paper discusses the evolution of cosmological gamma-ray burst (GRB) remnants, known as GRBR, following a gamma-ray burst event. The authors show that significant optical emission is expected, measurable hours after the event, and radio emission may be detectable days to weeks later. The flux at optical, X-ray, and other long wavelengths decays as a power of time, and the initial flux or magnitude, as well as the time-decay exponent, can help distinguish between different models of dissipative fireball evolution. The paper explores two main models for GRB remnants: the impulsive external shock model and the wind internal shock model. In the impulsive model, the initial energy input is impulsive, and the relativistic ejecta decelerate after sweeping up external mass. This leads to external and reverse shocks that radiate a large fraction of the initial energy. In the wind model, the initial energy input is continuous, and the resulting relativistic wind produces a GRB due to internal shocks. Both models produce significant amounts of softer radiation, mostly X-rays and optical, but sometimes also radio. The authors analyze the dynamical evolution of GRBR for both models, considering the effects of the initial energy input regime. They find that the temporal behavior of GRBR is dominated by the evolution of the Lorentz factor (Γ) and related dynamic quantities. In the impulsive model, Γ decreases as r^{-3/2} and r increases as t^{1/4}. In the wind model, Γ remains approximately constant, and r increases linearly with time. The paper also discusses the GRBR spectra from impulsive fireballs, considering three sub-cases. The first case involves only the forward blast wave radiating efficiently, leading to a synchrotron peak at a certain frequency. The second case considers both reverse and forward shocks as efficient radiators, leading to different spectral evolution regimes. The third case involves turbulent magnetic fields and different evolution of the magnetic field over time. For wind fireball models, the GRB spectra are discussed, with examples showing different spectral behaviors. The authors conclude that the optical detection of GRBR is possible with modest telescopes, and that radio and optical observations can help distinguish between different models. The paper emphasizes the importance of observing GRBR in different wavelengths to refine models and understand the physics of GRB remnants.This paper discusses the evolution of cosmological gamma-ray burst (GRB) remnants, known as GRBR, following a gamma-ray burst event. The authors show that significant optical emission is expected, measurable hours after the event, and radio emission may be detectable days to weeks later. The flux at optical, X-ray, and other long wavelengths decays as a power of time, and the initial flux or magnitude, as well as the time-decay exponent, can help distinguish between different models of dissipative fireball evolution. The paper explores two main models for GRB remnants: the impulsive external shock model and the wind internal shock model. In the impulsive model, the initial energy input is impulsive, and the relativistic ejecta decelerate after sweeping up external mass. This leads to external and reverse shocks that radiate a large fraction of the initial energy. In the wind model, the initial energy input is continuous, and the resulting relativistic wind produces a GRB due to internal shocks. Both models produce significant amounts of softer radiation, mostly X-rays and optical, but sometimes also radio. The authors analyze the dynamical evolution of GRBR for both models, considering the effects of the initial energy input regime. They find that the temporal behavior of GRBR is dominated by the evolution of the Lorentz factor (Γ) and related dynamic quantities. In the impulsive model, Γ decreases as r^{-3/2} and r increases as t^{1/4}. In the wind model, Γ remains approximately constant, and r increases linearly with time. The paper also discusses the GRBR spectra from impulsive fireballs, considering three sub-cases. The first case involves only the forward blast wave radiating efficiently, leading to a synchrotron peak at a certain frequency. The second case considers both reverse and forward shocks as efficient radiators, leading to different spectral evolution regimes. The third case involves turbulent magnetic fields and different evolution of the magnetic field over time. For wind fireball models, the GRB spectra are discussed, with examples showing different spectral behaviors. The authors conclude that the optical detection of GRBR is possible with modest telescopes, and that radio and optical observations can help distinguish between different models. The paper emphasizes the importance of observing GRBR in different wavelengths to refine models and understand the physics of GRB remnants.