Anisotropies in the angular power spectra of the Cosmic Microwave Background (CMB) temperature and polarization are sourced by inflationary perturbations on scales from 10^1 Mpc to 10^4 Mpc. Deviations of the CMB frequency spectrum from a black-body, instead, can probe inflationary perturbations on scales from 10^−4 Mpc to 10^−2 Mpc. These length scales are inaccessible to CMB and large-scale structure measurements. CMB spectral distortions, averaged over the whole sky, constrain the two-point function of primordial perturbations. Correlation of temperature and spectral distortion anisotropies, instead, can constrain their three-point function (making them a probe of primordial non-Gaussianity). In the first part of this thesis I study what is the level of sensitivity needed, by an experiment measuring the CMB frequency spectrum, to detect the running of the spectral index of inflationary perturbations. I then investigate what is the minimal contribution to the correlation function between temperature and spectral distortion anisotropies that is expected in standard inflationary scenarios. Finally, I discuss what are the secondary contributions (arising from late-time gravitational evolution) to such angular correlation, and how they could bias constraints on primordial non-Gaussianity.