Over the past decade, both the sensitivity and spectral dynamic range of radio telescopes have been greatly improved. These improvements have resulted in several new breakthroughs in searching for extragalactic radio recombination lines since the early detections toward M82 and NGC 253 two decades ago. It is shown that the line-to-continuum ratios observed in starburst nuclei provide good constraints on both the electron density and spatial size of the constituent HII regions. Our observations and analysis of the H92$\alpha$ lines at 3.5 cm suggest that the high density compact HII regions (n_e>10^4 cm^{-3}, d<= 1 pc) contribute a significant amount of line emission while the extended emission low density diffuse ionized gas stimulated by the galaxy backgrounds does not provide a good fit to the data. In the starburst nuclear regions, the distribution of electrons in the high density HII regions might deviate from local thermodynamic equilibrium (LTE), which could result in weak masering effects for the RRL emission at high frequencies. The non-LTE effect, in fact, provides an observational `filter' that selects a particular density region where the line emission is highly enhanced. In particular, the subcm RRLs are better tracers of high density HII regions which are invisible at longer wavelengths because of their large opacity. With no dust obscuring at radio wavelengths and the stability of the high density HII regions against the nuclear tidal force, the RRLs would be excellent tracers of the nuclear dynamics of galaxies.