One of the key motivations for the development of atomically resolved spectroscopic imaging scanning tunneling microscopy (SI-STM) has been to probe the electronic structure of cuprate high temperature superconductors. In both the d-wave superconducting (dSC) and the pseudogap (PG) phases of underdoped cuprates, two distinct classes of electronic states are observed using SI-STM. The first class consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor. These are detected below a lower energy scale |E| =Δ 0 and only upon a momentum space (k-space) arc which terminates near the lines connecting k - ±(π/a 00)toπ/ a 00 Below optimal doping, this "nodal" arc shrinks continuously with decreasing hole density. In both the dSC and PG phases, the only broken symmetries detected in the |E| ≤Δ 0 states are those of a d-wave superconductor. The second class of states occurs at energies near the pseudogap energy scale |E|∼Δ 1 which is associated conventionally with the "antinodal" states near k=±(0π. a/0).; and k=±(0π. a/0). We find that these states break the expected 90-rotational (C 4) symmetry of electronic structure within CuO 2 unit cells, at least down to 180°-rotational (C 2) symmetry (nematic) but in a spatially disordered fashion. This intra-unit-cell C 4 symmetry breaking coexists at |E| ∼Δ 1 with incommensurate conductance modulations locally breaking both rotational and translational symmetries (smectic). The characteristic wavevector Q of the latter is determined, empirically, by the k-space points where Bogoliubov quasiparticle interference terminates, and therefore evolves continuously with doping. The properties of these two classes of |E| ∼Δ 1 states are indistinguishable in the dSC and PG phases. To explain this segregation of k-space into the two regimes distinguished by the symmetries of their electronic states and their energy scales |E| ∼Δ 1 and |E|≤Δ 0, and to understand how this impacts the electronic phase diagram and the mechanism of high-T c superconductivity, represents one of a key challenges for cuprate studies. © 2012 The Physical Society of Japan.