We survey the use of spectroscopic imaging scanning tunneling microscopy (SI-STM) to probe the electronic structure of underdoped cuprates. Two distinct classes of electronic states are observed in both the d-wave superconducting (dSC) and the pseudogap (PG) phases. The first class consists of the dispersive Bogoliubov quasiparticle excitations of a homogeneous d-wave superconductor, existing below a lower energy scale E = Δ0. We find that the Bogoliubov quasiparticle interference (QPI) signatures of delocalized Cooper pairing are restricted to a k-space arc, which terminates near the lines connecting k = ±(π/a0, 0) to k = ±(0, π/a 0). This arc shrinks continuously with decreasing hole density such that Luttinger's theorem could be satisfied if it represents the front side of a hole-pocket that is bounded behind by the lines between k = ±(π/a0, 0) and k = ±(0, π/a0). In both phases, the only broken symmetries detected for the \E\ < Δ0 states are those of a d-wave superconductor. The second class of states occurs proximate to the PG energy scale E = Δ1. Here the non-dispersive electronic structure breaks the expected 90°-rotational symmetry of electronic structure within each unit cell, at least down to 180°-rotational symmetry. This electronic symmetry breaking was first detected as an electronic inequivalence at the two oxygen sites within each unit cell by using a measure of nematic (C2) symmetry. Incommensurate non-dispersive conductance modulations, locally breaking both rotational and translational symmetries, coexist with this intra-unit-cell electronic symmetry breaking at E = Δ1. Their characteristic wavevector Q is determined by the k-space points where Bogoliubov QPI terminates and therefore changes continuously with doping. The distinct broken electronic symmetry states (intraunit-cell and finite Q) coexisting at E ∼ Δ1 are found to be indistinguishable in the dSC and PG phases. The next challenge for SI-STM studies is to determine the relationship of the E ∼ Δ1 broken symmetry electronic states with the PG phase, and with the E < Δ0 states associated with Cooper pairing. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.