The definition, properties, and applications of the single-particle (electron) density $\ensuremath{\rho}(\mathrm{r})$ are discussed in this review. Since the discovery of Hohenberg-Kohn theorem, which gave a theoretical justification for considering $\ensuremath{\rho}(\mathrm{r})$, rather than the wave function, for studying both nondegenerate and degenerate ground states of many-electron systems, $\ensuremath{\rho}(\mathrm{r})$ has been acquiring increasing attention. The quantum subspace concept of Bader et al. has further highlighted $\ensuremath{\rho}(\mathrm{r})$ since a rigorous decomposition of the three-dimensional (3D) space of a molecule into quantum subspaces or virial fragments is possible, the boundaries of such subspaces being defined solely in terms of $\ensuremath{\rho}(\mathrm{r})$. Further, $\ensuremath{\rho}(\mathrm{r})$ is a very useful tool for studying various chemical phenomena. The successes and drawbacks of earlier models, such as Thomas-Fermi-Dirac, incorporating $\ensuremath{\rho}(\mathrm{r})$ are examined. The applications of $\ensuremath{\rho}(\mathrm{r})$ to a host of properties---such as chemical binding, molecular geometry, chemical reactivity, transferability, and correlation energy---are reviewed. There has been a recent trend in attempting to bypass the Schr\"odinger equation and directly consider single-particle densities and reduced density matrices, since most information of physical and chemical interest are encoded in these quantities. This approach, although beset with problems such as $N$-representability, and although unsuccessful at present, is likely to yield fresh concepts as well as shed new light on earlier ideas. Since charge density in 3D space is a fundamental quantum-mechanical observable, directly obtainable from experiment, and since its use in conjunction with density-functional theory and quantum fluid dynamics would provide broadly similar approaches in nuclear physics, atomic-molecular physics, and solid-state physics, it is not unduly optimistic to say that $\ensuremath{\rho}(\mathrm{r})$ may be the unifying link between the microscopic world and our perception of it.