VLBI observations show that the center of the nearby (~ 3.3 Mpc distant) spiral galaxy, M81, consists of a single elongated radio core, of dimensions 1000 × 4000 AU, with the major axis aligned, in projection, within 3° (<1σ) of the galaxy's rotation axis. This morphology can be interpreted in terms of an active galactic nucleus (AGN) with either a core-jet structure residing in M81's center or an accretion disk filling out the broadline region of this center. In contrast, the radio structure in the companion galaxy, M82, is very complex. VLBI observations of M82 yield the diameters and spectral index distribution of the hot spots, and the morphology and expansion velocity of the brightest hot spot, 41.9+58. Our results argue against the hot spots being core and jet condensations, or young supernovae (SNe), or typical supernova remnants (SNRs). We suggest that the hot spots in M82 are the remnants of stellar events that yielded some combination of SNRs and “exotic” objects.