Piezoresistance (PZR) is the change in the electrical resistivity of a solid induced by an applied mechanical stress. Its origin in bulk crystalline materials like silicon is principally a change in the electronic structure which leads to a modification of the effective mass of charge carriers. The past few years have seen a rising interest in the PZR properties of semiconductor nanostructures, motivated in part by claims of a giant PZR (GPZR) in silicon nanowires more than two orders of magnitude bigger than the known bulk effect. This review aims to present the controversy surrounding claims and counterclaims of GPZR in silicon nanostructures by summarizing the major works carried out over the past 10 years. The main conclusions to be drawn from the literature are that (i) reproducible evidence for a GPZR in ungated nanowires is limited; (ii) in gated nanowires, GPZR has been reproduced by several authors; (iii) the giant effect is fundamentally different from either the bulk silicon PZR or that resulting from quantum confinement, the evidence pointing to an electrostatic origin; (iv) released nanowires tend to have slightly larger PZR than unreleased nanowires; and (v) insufficient work has been performed on bottom-up grown nanowires to be able to rule out a fundamental difference in their properties when compared with top-down nanowires. On the basis of this, future possible research directions are suggested.