The ΛCDM model of cosmology predicts inevitable, weak distortions in the spectrum of the Cosmic Microwave Background (CMB) from that of a blackbody. However, no such deviations have been measured to date. In this talk, I focus on CMB spectral distortions arising from the cosmological epochs of recombination and cosmic dawn & reionization (collectively called EoR henceforth). A detection and measurement of these CMB spectral distortions will enable a better understanding of the thermal and ionization history of the Universe and help us probe redshifts that have never been directly observed thus far. I present a feasibility study for a ground-based detection of extremely weak, ripple-like additive features in the CMB spectrum created by photons emitted during cosmological recombination (900 < z < 7000). I introduce the Maximally Smooth (MS) function, an algorithm to distinguish smooth foregrounds from the ripple like signal. Using synthetic spectra, I demonstrate the efficacy of using MS functions over polynomials to separate foregrounds from the cosmological recombination signal. I also present GMOSS: Global model for the radio sky spectrum, a physically motivated model of the low-frequency radio sky. Using GMOSS I investigate the spectral complexity expected in foregrounds and the effect of the same on detection of the global redshifted 21-cm signal from EoR (6 < z < 150). Once again, I demonstrate the advantage of using MS functions over polynomials to separate foregrounds from the global EoR signal in mock-sky spectra. I conclude the talk with a brief discussion on design criteria for radio-telescopes seeking to detect distortions in the CMB spectrum arising from the epochs of recombination through reionization.