AbstractIn recent years the wavelength, dependence of the polarization in a number of Mira variables, semi-regular variables and red supergiants has been measured with resolutions between 0.3 and 300 A over the range 3300 to 11000 A. Variations are seen across molecular absorption bands, especially TiO bands, and across atomic absorption and emission lines, especially the Balmer lines. In most cases one can ignore or it is possible to eliminate the effects due to interstellar polarization, so that one can study the polarization mechanisms operating in the stellar atmosphere and environment. The stars Omicron Ceti. (Mira), V CVn (semi-regular variable) and Mu Cephei (M2 la), in addition to other stars similar to them, will be discussed in some detail.Models to explain the observed polarization consider that the continuum flux is polarized either by electron, molecular and/or grain scattering or by temperature variations and/or geometrical asymmetries over the stellar photosphere. This polarized radiation is affected by atomic and molecular absorption and emission processes at various geometric depths in the stellar atmosphere and envelope. High resolution spectropolarimetry promises, therefore, to be a power-rul tool for studying stratification effects in these stars.