There is a fairly strong presumption that the underlying process is accretion of matter onto a supermassive black hole, but progressing from there to a believable detailed theory has proved very difficult. One of the problems has been the complex and confusing phenomenology, and a bewildering variety of "types" of AGN.
I have written a number of papers working towards a unified scheme for AGN (see for example my review papers in 19.) A popular idea is that narrow-line AGN are the same as quasars but hidden by an obscuring "torus" of dust, and that in fact most quasars are obscured, and are seen as luminous IR galaxies.
All these things are a sign of the disc breaking down in the central regions.
After some years of giving conference talks on this topic, I have finally written a substantial paper, in which I propose that the UV peak of the Big Blue Bump is actually a false peak caused by reflection from dense clouds surrounding the accretion disc, with the true peak being at 300 Angstroms. One of the goals of the UKIDSS survey has been to break past z=6.4, which has been the quasar redshift barrier for many years. we did this in spectacular fashion, finding a quasar at z=7.085 (Mortlock et al 2011).
Then in this 2008 paper led by Makoto Kishimoto, we showed that after removing dust emission using cunning polarimetric techniques, the IR spectra of quasars show pretty much the long-predicted nu**1/3 shape.
However there are serious problems for accretion discs models in other places.
I am currently working on tests of the warped disc idea, especially with a combined WISE-UKIDSS-SDSS sample. Potentially this holds clues to the Physics of AGN we can't get any other way.
My current PDRA Isaac Roseboom just led a paper deriving the distribution of covering factors for high luminosity quasars, showing pretty good agreement with the warped disc model. My 1987 Nature paper on NGC 4051 had the first light curve of high enough quality to take this seriously, but showed a featureless power law power spectrum.
I have simultaneously been part of developing this idea, and of criticising it.
Example papers are from 1991, 1999, and a recent (2010) Ap J paper looking at the idea of obscuration by warped discs resulting from chaotic accretion.