  \lco{} is known for its two-step spin crossover as a function of temperature.
Despite efforts spanning over half a century, the origin of this phenomenon is
still debated, particularly regarding how the microscopic spin states are
involved in the observed macroscopic two-step spin crossover. High magnetic
field studies on LaCoO$_{3}$ are performed because the magnetic field-induced
spin crossover is induced, where the magnetic excited states become more stable
in high magnetic fields than the non-magnetic ground states. This review
focuses on the findings in LaCoO$_{3}$ at high magnetic fields over the last
decade. A complex phase diagram has been revealed at high magnetic fields
instead of solving the conventional problem of LaCoO$_{3}$. It suggests that
appreciable spin state correlations are in play in LaCoO$_{3}$. The possibility
of exciton condensation is also discussed.
