Calculations of energy levels, radiative rates and lifetimes are reported for 17 F-like ions with 37 $\le$ Z $\le$ 53. For brevity, results are only presented among the lowest 113 levels of the 2s$^2$2p$^5$, 2s2p$^6$, 2s$^2$2p$^4$3$\ell$, 2s2p$^5$3$\ell$, and 2p$^6$3$\ell$ configurations, although the calculations have been performed for up to 501 levels in each ion. The general-purpose relativistic atomic structure package (GRASP) has been adopted for the calculations, and radiative rates (along with oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are made with earlier available experimental and theoretical energies, although these are limited to only a few levels for most ions. Therefore for additional accuracy assessments, particularly for energy levels, analogous calculations have been performed with the Flexible Atomic Code (FAC), for up to 72~259 levels. Limited previous results are available for radiative rates for comparison purposes, and no large discrepancy is observed for any transition and/or ion.