  This article will give an overview on both theoretical and experimental
developments concerning states with lattice symmetry breaking in the cuprate
high-temperature superconductors. Recent experiments have provided evidence for
states with broken rotation as well as translation symmetry, and will be
discussed in terms of nematic and stripe physics. Of particular importance here
are results obtained using the techniques of neutron and x-ray scattering and
scanning tunneling spectroscopy. Ideas on the origin of lattice-symmetry-broken
states will be reviewed, and effective models accounting for various
experimentally observed phenomena will be summarized. These include both
weak-coupling and strong-coupling approaches, with a discussion on their
distinctions and connections. The collected experimental data indicate that the
tendency toward uni-directional stripe-like ordering is common to underdoped
cuprates, but becomes weaker with increasing number of adjacent CuO_2 layers.
