Recent observational results confirm that many of the physical processes which are known to occur in the Sun also occur among late-type stars in general. One such process is the continuous loss of mass from a star in the form of a wind. There now exists an abundance of either direct or circumstantial evidence which suggests that most (if not all) stars in the cool portion of the HR diagram possess winds. An attempt is made to assess the current state of theoretical understanding of mass loss from two distinctly different classes of late-type stars: the post-main-sequence giant/supergiant stars and the pre-main-sequence T Tauri stars. Toward this end, the observationally inferred properties of the wind associated with each of the two stellar classes under consideration are summarized and compared against the predictions of existing theoretical models. Although considerable progress has been made in attempting to identify the mechanisms responsible for mass loss from cool stars, many fundamental problems remain to be solved