  The phenomenon of fractional quantum Hall effect (FQHE) was first
experimentally observed 33 years ago. FQHE involves strong Coulomb interactions
and correlations among the electrons, which leads to quasiparticles with
fractional elementary charge. Three decades later, the field of FQHE is still
active with new discoveries and new technical developments. A significant
portion of attention in FQHE has been dedicated to filling factor 5/2 state,
for its unusual even denominator and possible application in topological
quantum computation. Traditionally FQHE has been observed in high mobility GaAs
heterostructure, but new materials such as graphene also open up a new area for
FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in
graphene.
