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The many phases of 2D electrons in high magnetic fields

Two-dimensional electron systems exposed to low temperatures and high magnetic fields exhibit a rich spectrum of novel electronic phases. The highly correlated quantum liquids underlying the fractional quantum Hall effect (FQHE) dominate this region of phase space. Beyond the primitive Laughlin liquids, experiments have unraveled a multitude of higher order fractions whose origin and mutual relationships continue to be debated. The existence of the electron spin has led to the appearance of yet other electron liquids, some with even-denominator quantum numbers and novel properties. In the lowest Landau level, at half-filling, strong experimental features point towards the existence of yet another state; distinctly different from a FQHE liquid. At the highest fields and lowest electron concentration an insulating phase prevails as the temperature drops towards zero. This phase has been shown to engulf the v = 1/5 Laughlin liquid and is postulated to reflect the sought-after electron solid, pinned to residual impurities. Such an assignment remains controversial and alternative origins have been proposed. Recent experiments are expanding out of the plane elucidating electron correlation phenomena as the third dimension is added successively. This paper summarizes the highlights of the past decade and covers some recent developments. It focuses on experiments and stresses the progress in electronic transport measurements in this active field of research.