  This review gives a rather general discussion of high temperature
superconductors as an example of a strongly correlated material. The argument
is made that in view of the many examples of unconventional superconductors
discovered in the past twenty years, we should no longer be surprised that
superconductivity emerges as a highly competitive ground state in systems where
Coulomb repulsion plays a dominant role. The physics of the cuprates is
discussed, emphasizing the unusual pseudogap phase in the underdoped region. It
is argued that the resonating valence bond (RVB) picture, as formulated using
gauge theory with fermionic and bosonic matter fields, gives an adequate
physical understanding, even though many details are beyond the powers of
current calculational tools. The recent discovery of quantum oscillations in a
high magnetic field is discussed in this context. Meanwhile, the problem of the
quantum spin liquid (a spin system with antiferromagnetic coupling which
refuses to order even at zero temperature) is a somewhat simpler version of the
high $T_c$ problem where significant progress has been made recently. It is
understood that the existence of matter fields can lead to de-confinement of
the U(1) gauge theory in 2+1 dimensions, and novel new particles (called
fractionalized particles), such as fermionic spinons which carry spin ${1\over
2}$ and no charge, and gapless gauge bosons can emerge to create a new critical
state at low energies. We even have a couple of real materials where such a
scenario may be realized experimentally. The article ends with answers to
questions such as: what limits $T_c$ if pairing is driven by an electronic
energy scale? why is the high $T_c$ problem hard? why is there no consensus?
and why is the high $T_c$ problem important?
