The solution-liquid-solid (SLS) and related solution-based methods for the synthesis of semiconductor nanowires and nanorods are reviewed. Since its discovery in 1995, the SLS mechanism and its close variants have provided a nearly general strategy for the growth of pseudo-one-dimensional nanocrystals. The various metallic-catalyst nanoparticles employed are summarized, as are the syntheses of III-V, II-VI, IV-VI, group IV, ternary, and other nanorods and nanowires. The formation of axial heterojunctions, core/shell nanowires, and doping are also described. The related supercritical-fluid-liquid-solid (SFLS), electrically controlled SLS, flow-based SLS, and solution-solid-solid (SSS) methods are discussed, and the crystallographic characteristics of the wires and rods grown by these methods are summarized. The presentation of optical and electronic properties emphasizes electronic structures, absorption cross sections, polarization anisotropies, and charge-carrier dynamics, including photoluminescence intermittency (blinking) and photoluminescence modulation by charges and electric fields. Finally, developing applications for the pseudo-one-dimensional nanostructures in field-effect transistors, lithium-ion batteries, photocathodes, photovoltaics, and photodetection are discussed.