  We argue that aspects of the anomalous, low temperature, spin and charge
dynamics of the high temperature superconductors can be understood by studying
the corresponding physics of undoped Mott insulators. Such insulators display a
quantum transition from a magnetically ordered Neel state to a confining
paramagnet with a spin gap; the latter state has bond-centered charge order, a
low energy S=1 spin exciton, confinement of S=1/2 spinons, and a free S=1/2
moment near non-magnetic impurities. We discuss how these characteristics, and
the quantum phase transitions, evolve upon doping the insulator into a d-wave
superconductor. This theoretical framework was used to make a number of
predictions for STM measurements and for the phase diagram of the doped Mott
insulator in an applied magnetic field.
