  Highly accreting quasars are characterized by distinguishing properties in
the 4D eigenvector 1 parameter space that make them easily recognizable over a
broad range range of redshift and luminosity. The 4D eigenvector 1 approach
allows us to define selection criteria that go beyond the restriction to Narrow
Line Seyfert 1s identified at low redshift. These criteria are probably able to
isolate sources with a defined physical structure i.e., a geometrically thick,
optically thick advection-dominated accretion disk (a "slim" disk). We stress
that the importance of highly accreting quasars goes beyond the understanding
of the details of their physics: their Eddington ratio is expected to saturate
toward values of order unity, making them possible cosmological probes.
