  In LiHo_xY_{1-x}F4, the magnetic Holmium Ho^{3+} ions behave as effective
Ising spins that can point parallel or antiparallel to the crystalline c-axis.
The predominant inter-Holmium interaction is dipolar, while the Y^{3+} ions are
non-magnetic. The application of a magnetic field Bx transverse to the c-axis
Ising direction leads to quantum spin-flip fluctuations, making this material a
rare physical realization of the celebrated transverse field Ising model. The
problems of classical and transverse-field-induced quantum phase transitions in
LiHo_xY_{1-x}F_4 in the dipolar ferromagnetic (x=1), diluted ferromagnetic
(0.25 <~ x < 1) and highly diluted x<~0.25 dipolar spin glass regimes have
attracted much experimental and theoretical interest over the past twenty-five
years. Two questions have received particular attention: (i) is there an {\it
antiglass} (quantum disordered) phase at low Ho^{3+} concentration and (ii)
what is the mechanism responsible for the fast Bx-induced destruction of the
ferromagnetic (0.25 <~ x < 1) and spin glass (x <~ 0.25) phases? This paper
reviews some of the recent theoretical and experimental progress in our
understanding of the collective phenomena at play in LiHo_xY_{1-x}F4, in both
zero and nonzero Bx.
