The scattering of positrons by simple atoms such as hydrogen (which is of particular interest in gamma-ray astrophysics) or lithium are fundamental atomic collision processes that provide an attractive testing ground for scattering theories. In spite of the relative simplicity of there target atoms, calculating accurate cross sections for these collision systems has been far from trivial, and significant advances have been made even within the past several years. Making the corresponding measurements has been at least as challenging. The Wayne State positron scattering group has been involved in measuring total, positronium formation, and differential elastic cross sections for positrons of 1 to few hundred eV colliding with atoms, including the simple ones mentioned above, and molecules. Some recent developments in this research will be discussed.