Methyl fluoride is a prototypical symmetric-top molecule. Despite the fact that its rotational spectrum has been largely investigated, centrifugal-distortion constants were determined only up to the sextic terms. The present investigation demonstrates the importance of sub-Doppler measurements in the terahertz region not only for deriving higher-order centrifugal-distortion terms but also for revising the parameters available in the literature. The Lamb-dip technique has been exploited for obtaining sub-Doppler resolution in the 102 GHz to 1.2 THz frequency range, thus allowing for the improvement of all spectroscopic parameters. Furthermore, the hyperfine structure due to fluorine and hydrogens has been resolved, thus enabling the determination of the corresponding spin-rotation constants with an accuracy rivaling that obtained by molecular-beam electric resonance measurements and of the dipolar spin-spin coupling constants for the first time. The prediction and analysis of hyperfine structures were guided and supported by high-level quantum-chemical calculations of the parameters involved.