  The study of compact active galactic nuclei (AGN) that possess convex radio
spectra (the gigahertz-peaked spectrum radio sources) offers a unique
opportunity to probe both the early evolutionary stages of relativistic AGN
jets and their immediate nuclear environments. In this article I trace Ken
Kellermann's early investigations of these sources, which played a major role
in justifying the development of modern-day VLBI techniques. I describe how our
understanding of these AGN has progressed since Kellermann's early discoveries,
and discuss several ways in which the current classification scheme can be
simplified to reflect intrinsic source characteristics, rather than
observer-biased quantities. Finally, I discuss recent results from the VLBA 2
cm survey concerning the relativistic jet kinematics of the two-sided
peaked-spectrum sources 4C +12.50 (PKS 1345+125) and OQ 208 (1404+286).
