We have used digital in-line holography (DIH) with numerical reconstruction to image micrometer-sized latex spheres as well as ferrimagnetic beads suspended in gelatin. We have examined in detail theoretically and experimentally the conditions necessary to achieve submicrometer resolution of holographic reconstructions. We found that both transparent and opaque particles could be imaged with a resolution that was limited only by the wavelength of the light used. Simple inspection of intensity profiles through a particle allowed an estimate to be made of the particle's three position coordinates within an accuracy of a few hundred nanometers. When the derivative of a second-order polynomial fitted to the intensity profiles was taken, the X, Y, Z position coordinates of particles could be determined within +/-50 nm. More-accurate positional resolution should be possible with the help of more-advanced computer averaging techniques. Because a single hologram can give information about a large collection of distributed particles, DIH offers the prospect of a powerful new tool for three-dimensional tracking of particles.