  This article presents a review on the theoretical and the experimental
developments on macroscopic quantum tunneling and phase transition of the
escape rate in spin systems. We present the basic ideas with simplified
calculations so that it is readable to both specialists and nonspecialists in
this area of research. A brief derivation of the path integral formulation of
quantum mechanics in its original form using the orthonormal position and
momentum basis is reviewed. For spin systems such as single molecule magnets,
the formulation of path integral requires the use of non-orthonormal spin
coherent state in $(2s+1)$ dimensional Hilbert space, the coordinate
independent and the coordinate dependent form of the spin coherent state path
integral is derived. These two forms of spin coherent state path integral are
applied to the tunneling of single molecule magnets through its magnetic
anisotropy barrier. Most experimental and numerical results are presented. The
suppression of tunneling for half-odd integer spin (spin-parity effect) at zero
magnetic field is derived from both forms, which shows that this result
(spin-parity effect) is independent of the coordinate. At nonzero magnetic
field we present both the experimental and the theoretical results of the
oscillation of tunneling splitting as a function of the applied magnetic field
applied along the spin hard anisotropy axis direction. The experimental and the
theoretical results of the tunneling in antiferromagnetic exchange coupled
dimer model are also reviewed. As the spin coherent state path integral
formalism is a semi-classical method, an alternative exact mapping of a spin
system to a particle in a potential field (effective potential method) is
derived. This effective potential method allows for the investigation of phase
transition of the escape rate in spin systems.
