We describe a Monte Carlo code that accurately treats multiple scattering, absorption, and polarization by dust, and use this code to calculate images of dusty disks around young stellar objects. We present some approximate analytic results that describe the behavior of the Monte Carlo calculations. A geometrically thin disk illuminated by a central T Tauri star scatters very little light at distances of many AU from the star. Viewed at any inclination, the flux scattered by such a disk at the distance to the nearest star-forming region will be overwhelmed by the stellar image. An optically thick disk that has a "flaring" surface may be observable, especially if viewed nearly edge-on so that the stellar source becomes occulted. An optically thin disk with a finite opening angle, similar to the one surrounding beta-Pictoris, is about as observable as the typical flared optically thick disk at a similar distance from the Earth. The polarization position angle is perpendicular to the disk plane in all of the models, in contrast to observations of many young stellar objects which have the position angle oriented parallel to the presumed disk plane. We suggest that the scattered light structures observed around many pre-main-sequence objects are dusty envelopes rather than disks.