A theoretical investigation of the electromagnetic responses of a slanted chiral sculptured thin film (STF) to both plane waves and finite sources (such as optical beams and dipolar sources) was carried out. First, a rigorous coupled--wave analysis was implemented with algorithmic stability to obtain the planewave response; second, the angular--spectrum decomposition of the incident field was exploited to represent the reflected and the transmitted fields. The most prominent feature of the planewave responses is the circular Bragg phenomenon which is partially specular and angularly asymmetric for slanted, but nor for unslanted, chiral STFs. Correspondingly, the far--field radiation pattern of a Beltrami source configuration is spatially asymmetric in the presence of a slanted chiral STF. Also, optical beams are laterally shifted on reflection by chiral STFs. Two types of lateral shifts of Gaussian beams were studied: one is related to the Bragg reflection of co-handed beams, and the other is the Goos-Hanchen shift on total reflection.