This article provides a comprehensive review of current research activities that concentrate on one-dimensional (1D) nanostructures—wires, rods, belts, and tubes—whose lateral dimensions fall anywhere in the range of 1 to 100 nm. We devote the most attention to 1D nanostructures that have been synthesized in relatively copious quantities using chemical methods. We begin this article with an overview of synthetic strategies that have been exploited to achieve 1D growth. We then elaborate on these approaches in the following four sections: i) anisotropic growth dictated by the crystallographic structure of a solid material; ii) anisotropic growth confined and directed by various templates; iii) anisotropic growth kinetically controlled by supersaturation or through the use of an appropriate capping reagent; and iv) new concepts not yet fully demonstrated, but with long-term potential in generating 1D nanostructures. Following is a discussion of techniques for generating various types of important heterostructured nanowires. By the end of this article, we highlight a range of unique properties (e.g., thermal, mechanical, electronic, optoelectronic, optical, nonlinear optical, and field emission) associated with different types of 1D nanostructures. We also briefly discuss a number of methods potentially useful for assembling 1D nanostructures into functional devices based on crossbar junctions, and complex architectures such as 2D and 3D periodic lattices. We conclude this review with personal perspectives on the directions towards which future research on this new class of nanostructured materials might be directed.