  The hidden order developing below 17.5K in the heavy fermion material URu2Si2
has eluded identification for over twenty five years. This paper will review
the recent theory of ``hastatic order,'' a novel two-component order parameter
capturing the hybridization between half-integer spin (Kramers) conduction
electrons and the non-Kramers 5f^2 Ising local moments, as strongly indicated
by the observation of Ising quasiparticles in de Haas-van Alphen measurements.
Hastatic order differs from conventional magnetism as it is a spinor order that
breaks both single and double time-reversal symmetry by mixing states of
different Kramers parity. The broken time-reversal symmetry simply explains
both the pseudo-Goldstone mode between the hidden order and antiferromagnetic
phases and the nematic order seen in torque magnetometry. The spinorial nature
of the hybridization also explains how the Kondo effect gives a phase
transition, with the hybridization gap turning on at the hidden order
transition as seen in scanning tunneling microscopy. Hastatic order also has a
number of new predictions: a basal-plane magnetic moment of order .01\mu_B, a
gap to longitudinal spin fluctuations that vanishes continuously at the first
order antiferromagnetic transition and a narrow resonant nematic feature in the
scanning tunneling spectra.
