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Superconductor-insulator (SI) transitions in ultra-thin metal films have attracted substantial attention over the last decade because of the possibility that they are quantum phase transitions, and because they may be simple model systems for phenomena found in high temperature superconductors. The elegant bosonic picture of these transitions that was proposed some years ago is now only in qualitative agreement with measurements. In particular, the critical resistance appears not to be universal, and values of critical exponents are different from theoretical expectations. There are also indications that the phase diagram may include a significant metallic phase separating the superconducting and insulating phases, and that the transition may have a percolative aspect. In this talk, data on superconductor-insulator transitions, both supporting and contradicting the quantum critical point picture, will be reviewed critically. Aspects of these two dimensional metallic systems relevant to high temperature superconductivity will also be discussed.
