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Every finite family of (straight) lines in the projective plane, not forming a pencil, is well know to have at least one "ordinary point" –– that is, a point common to precisely two of the lines. A line of a family is said to be "omittable" if it contains no ordinary point of the family. Despite the large extent of work on ordinary points and related topics, very little has been published concerning omittable lines. A survey of the published results is presented, together with several new ones.