  As Setti & Woltjer noted back in 1973, quasars could be used to construct the
Hubble diagram but the actual application was not that straightforward. It took
years to implement the idea successfully. Most of the ways to use quasars for
cosmology now require an advanced understanding of their structure, step by
step. We briefly review this progress, with unavoidable personal bias, and
concentrate on bright unobscured sources. We will mention the problem of the
gas flow character close to the innermost stable circular orbit close to the
black hole, discussed 50 years ago, which later led to the development of the
slim disk scenario, but was recently revived in the context of Magnetically
Arrested Disks (MAD) and Standard and Normal Evolution (SANE) disk models. We
also discuss the hot/warm corona issue, which is still under discussion and
complicates the analysis of the X-ray reflection. We present the scenario of
the formation of the low ionization part of the Broad Line Region as a mostly
failed wind powered by radiation pressure acting on dust (FRADO - Failed
Radiatively Driven Dusty Outflow model). Next, we discuss the cosmological
constraints that are currently achievable with quasars, mostly concentrating on
light echo methods (continuum time delays and spectral line time delays with
respect to the continuum) which are (or should be) incorporating the progress
mentioned above. Finally, we briefly mention future prospects in this
direction.
