Gadolinium(III) complexes are often used in clinical MRI to increase contrast by selectively relaxing the water molecules near the complex. There is a desire to improve the sensitivity (relaxivity) of these contrast agents in order to detect molecular targets. This tutorial review describes the molecular factors that contribute to relaxivity and illustrates with recent examples how these can be optimized. It may be of interest to senior undergraduates and more advanced researchers interested in lanthanide chemistry, biophysics, and/or molecular imaging.