Low density plasmas have long been of interest as a potential medium for particle acceleration since relativistic plasma waves are capable of supporting electric fields greater than 100 GeV/m. The physics of particle acceleration using plasmas will be reviewed, and new results will be discussed which have demonstrated that relatively narrow energy spread (<3%) beams having energies greater than 100 MeV can be produced from femtosecond laser plasma interactions. Future experiments and potential applications will also be discussed.