In this thesis, a new technique for studying convection is developed using relative line-shifts. The technique is tested using the sun's visible flux spectrum and the most current FeI line positions available, and can be applied at significantly lower spectral resolutions and signal-to-noise ratios than has been done previously. These line-shifts show a clear dependence on both line strength and wavelength. Similar observations in the solar intensity spectrum demonstrate that the effects of limb darkening on the line-shifts are relatively minor. Because the solar intensity spectrum has been observed well into the infrared, it has been used to study the line-shift techniques over the broadest possible spectral region. The FeI line-core shift distributions show clear evidence of a dependence on line strength at all wavelengths, and sensitivities to wavelength are found at shorter wavelengths. Line-shifts for 1323 CO lines between 2.2 and 5.5 microns are also determined. Clear evidence of a dependence on line strength is found at all wavelengths, and interesting line-shift behavior is found when the excitation energy and quantum numbers of the CO transitions are examined. A similar study of CO and OH line-shifts is done using a sunspot umbral spectrum, and the convective motions are found to be greatly suppressed. Line-shifts are also examined in the infrared spectrum of six cool giant stars. The vigorous nature of convection seems to decline with Teff, which is consistent with expectations.