We outline recent developments in biological single-molecule fluorescence detection with particular emphasis on observations by ratiometric fluorescence resonance energy transfer (FRET) of biomolecules freely diffusing in solution. Single-molecule-diffusion methodologies were developed to minimize perturbations introduced by interactions between molecules and surfaces. Confocal microscopy is used in combination with sensitive detectors to observe bursts of photons from fluorescently labeled biomolecules as they diffuse through the focal volume. These bursts are analyzed to extract ratiometric observables such as FRET efficiency and polarization anisotropy. We describe the development of single-molecule FRET methodology and its application to the observation of the Förster distance dependence and the study of protein folding and polymer physics problems. Finally, we discuss future advances in data acquisition and analysis techniques that can provide a more complete picture of the accessible molecular information.