  Superconductor-insulator/metal transition (SIT/SMT) as a paradigm of quantum
phase transition has been a research highlight over the last three decades.
Benefit from recent developments in the fabrication and measurements of 2D
superconducting films and nanodevices, unprecedented quantum phenomena have
been revealed in the quantum phase transitions of 2D superconductors. In this
review, we introduce the recent progress on quantum phase transitions in 2D
superconductors, focusing on the quantum Griffiths singularity (QGS) and
anomalous metal state. Characterized by a divergent critical exponent when
approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline
Ga films and subsequently detected in various 2D superconductors. The
universality of QGS indicates the profound influence of quenched disorder on
quantum phase transitions. Besides, in a 2D superconducting system, whether a
metallic ground state can exist is a long-sought mystery. Recently, the
charge-2e quantum oscillations are observed in nanopatterned superconducting
films, indicating the bosonic nature of the anomalous metal state and ending
the debate on whether bosons can exist as a metal. The evidences of the
anomalous metal states have also been reported in crystalline epitaxial thin
films and exfoliated nanoflakes, as well as granular composite films. High
quality filters are used in these works to exclude the influence of external
high frequency noises in ultralow temperature measurements. The observations of
QGS and metallic ground states in 2D superconductors not only reveal the
prominent role of quantum fluctuations and dissipations but also provide new
perspective to explore quantum phase transitions in superconducting systems.
