Atomically resolved spectroscopic imaging STM (SI-STM) has played a pivotal role in visualization of 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 types of electronic states are observed when using SI-STM. The first consists of the dispersive Bogoliubov quasiparticles of a homogeneous d-wave superconductor existing in an energy range$\vert E\vert \le \varDelta _0 and only upon an arc in momentum space (k-space) that terminates close to the lines connecting k= \pm (\pi /a_0,0) to k= \pm (0, \pi /a_0). This ‘nodal’ arc shrinks continuously as electron density increases towards half filling. In both phases, the only broken symmetries detected in the\vert E\vert \le \varDelta ₀ states are those of a d-wave superconductor. The second type of electronic state occurs near the pseudogap energy scale\vert E\vert \sim \varDelta ₠or equivalently near the ‘antinodal’ regions k= \pm (\pi /a_0,0) and k= \pm (0, \pi /a_0). These states break the expected 90\circ -rotational (C:4 ) symmetry of electronic structure within each CuO:2 unit cell, at least down to 180\circ -rotational (C:2 ), symmetry. This intra-unit-cell symmetry breaking is interleaved with the incommensurate conductance modulations locally breaking both rotational and translational symmetries. Their wavevector S is always found to be determined by the k-space points where Bogoliubov quasiparticle interference terminates along the line joining\mathbf k =(0,\pm \pi /a_0) to\mathbf k =(\pm \pi /a_0,0), and thus diminishes continuously with doping. The symmetry properties of these\vert E\vert \sim \varDelta _1 states are indistinguishable in the dSC and PG phases. While the relationship between the\vert E\vert \sim \varDelta _1 broken symmetry states and the\vert E\vert \le \varDelta ₀$ Bogoliubov quasiparticles of the homogeneous superconductor is not yet fully understood, these two sets of phenomena are linked inextricably because the k-space locations where the latter disappears are always linked by the modulation wavevectors of the former. © 2015, Springer-Verlag Berlin Heidelberg.