  Recent observations of broken symmetries have partly demystified the
pseudogap phase. Here we review evidence for long-range intra-unit-cell(IUC)
nematic order and its unexpectedly strong coupling to the phase of the
fluctuating stripes in the pseudogap states of underdoped
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. In particular, we focus on the analysis
techniques that reveal this evidence in scanning tunneling spectroscopy data,
the definition of the extracted IUC nematic order parameter, and a
phenomenological theory of the coupling between the IUC nematic order and the
previously reported coexisting fluctuating stripes. We also present a
microscopic mechanism of IUC nematic order driven by on-site and near-neighbor
repulsions. Finally we discuss open questions in the context of these results.
