Active galactic nuclei (AGNs) are distant, powerful sources of radiation over the entire electromagnetic spectrum, from radio waves to gamma-rays. There is much evidence that they are driven by gravitational accretion of stars, dust, and gas, onto central massive black holes (MBHs) imprisoning anywhere from $\~$ 수식 이미지1 to $\~$ 수식 이미지10,000 million solar masses; such objects may naturally form in the centers of galaxies during their normal dynamical evolution. A small fraction of AGNs, of the radio-loud type (RLAGNs), are somehow able to generate powerful synchrotron-emitting structures (cores, jets, lobes) with sizes ranging from pc to Mpc. A brief summary of AGN observations and theories is given, with an emphasis on RLAGNs. Preliminary results from the imaging of 10000 extragalactic radio sources observed in the MITVLA snapshot survey, and from a new analytic theory of the time-variable power output from Kerr black hole magnetospheres, are presented. To better understand the complex physical processes within the central engines of AGNs, it is important to confront the observations with theories, from the viewpoint of analyzing the time-variable behaviours of AGNs - which have been recorded over both 'short' human (10 0-10 9s) and 'long' cosmic (10 13 - 10 17 s) timescales. Some key ingredients of a basic mathematical formalism are outlined, which may help in building detailed Monte-Carlo models of evolving AGN populations; such numerical calculations should be potentially important tools for useful interpretation of the large amounts of statistical data now publicly available for both AGNs and RLAGNs.