  The advent of the Very Long Baseline Array and its phase-referencing
capability have enabled milliarcsecond-scale imaging of radio sources at
sub-millijansky sensitivity, opening the door to high-resolution imaging of
Seyfert galaxies. Over the last few years, this has led to a number of
interesting new results that shed light on the characteristics of the inner
cores of Seyfert galaxies. These include the following: (1) classical Seyfert
galaxies with steep radio spectra have a strong tendency to exhibit radio jets
at milliarcsecond scales, sometimes with considerable curvature in the jets;
(2) apparent speeds of jets imaged at multiple epochs generally are
considerably less than c, often in the vicinity of 0.1c or less, although there
sometimes are faster motions seen after strong outbursts; and (3) lower
luminosity Seyfert galaxies have a much stronger tendency to show flat or
somewhat inverted radio spectra, usually are unresolved on milliarcsecond
scales, and probably are dominated by a combination of low-radiative-efficiency
accretion flows and very compact radio jets. This paper discusses some examples
that illustrate these properties, and summarizes some of what we have learned
about weak active galaxies on milliarcsecond scales.
