High-resolution Doppler-resolved spectroscopy has opened up a new window into the atmospheres of both transiting and non-transiting exoplanets. While the 'classical' cross-correlation approach is efficient for finding atomic and molecular species, it is quite limited with its inability to recover quantitative information on the atmosphere such as abundances and temperature profiles, nor can it place statistically robust uncertainties on the quantities it can measure (e.g. velocities, detection significances). Recent pioneering efforts have sought to develop likelihood ‘mappings’ from the cross-correlation function, that can be used to directly compare model fits to high-resolution data sets thus solving these issues. Here, I will outline a framework based purely on a simple Gaussian likelihood, remarkably similar to the techniques that have been applied to transit light curves for over a decade. These can be used to explore the posterior distribution of parametrised model atmospheres in a statistically rigorous way. However, one important and distinct problem remains for high-resolution retrievals; the methods used for filtering out the stellar and telluric lines from the data also filters the underlying exoplanet's signal. I will discuss a simple and fast technique to  address this problem that enables retrievals from data filtered through common methods such as SysRem and PCA. Finally, I will demonstrate this framework on observations of the ultra-hot Jupiter WASP-121b, including constraints on the abundances and temperature profile of the atmosphere.