In a combination tutorial and research paper, propagation aspects of transmission at infrared (IR) frequencies for wireless in-building communications are explored. The tutorial section of the paper presents basic principles of propagation at IR, a comparison with indoor radio propagation, and the derivation of the channel's baseband model. The research aspect of the paper reports on the results of recent frequency response measurements at eight different sites in a university building. A major result shows that the indoor wireless optical channel is very dynamic, with great variations in the channel's characteristics for data collected in different rooms, in different locations within the same room, and for different orientations of the optical receiver at the same location of the same room. Numerical values of the channel's relative path loss and 3 dB bandwidth, along with frequency response plots covering a wide range of conditions, are presented and discussed. Finally, on the basis of the results of measurements, schemes for improving the performance of future wireless in-building optical transceivers are proposed.