High-Q optical whispering-gallery modes TE(TM)(lmq) in spheroidal dielectric microresonators are shown to be equivalent to precessing circular modes TE (TM)(llq') with the rate of precession depending on the value of the residual resonator nonsphericity. This approach gives a natural interpretation to the characteristic two-lobe emission patterns of these modes with prism couplers. Spatial recognition of different modes on the basis of their emission patterns facilitates optimal coupling to selected modes, which is of interest for applications. Experimental results on the observation of two-lobe emission patterns and imaging of internal mode field distributions are presented. The feasibility of a single-prism transient filter and an optical delay line based on precessing modes is discussed.