Two-dimensional electrons continue to surprise us, this time from 
very high Landau levels.  Following original experiments on oscillatory 
microwave photoresistance (OMP), two groups recently reported 
an observation of a periodic series of "zero-resistance" states (ZRS). 
Such states evolve from the OMP minima in a very clean 2D electron gas 
subjected to crossed microwave (f > 30 GHz) and weak magnetic 
(B < 0.5 T) fields at low temperatures (T ~ 1 K). ZRS are positioned 
about the magnetic fields where the microwave frequency somewhat 
exceeds integer multiple of the cyclotron frequency and are 
characterized by an exponentially small low-temperature diagonal 
resistance and a classical Hall resistance. More recently we have 
shown that ZRS correspond to vanishing conductivity measured in 
Corbino samples. Combining both the resistivity and conductivity data, 
we conclude that our findings represent a new dissipationless effect 
in 2D electronic transport. This talk will survey the experimental 
development from OMP to ZRS as the sample mobility is improved, 
present the resistivity and the conductivity results, and briefly 
discuss selected theoretical proposals aimed to elucidate its origin.