The abnormal or freak waves of great height present a serious danger for ships and sea oil platforms. In this review we discuss the characteristics of freak waves. The freak waves are interested for us as the targets for an azimuth scan pulsed microwave radar. In our research, first of all, we consider the geometrical shapes of two-dimensional models of abnormal waves and briefly three-dimensional models. To the well-known classification of abnormal waves: Singular Wave Tower, Three Sisters, White Wall we added two variants of crests: smooth or three-cornered. Also, we briefly study the temporal attributes of abnormal waves. In the end of our research, we propose the criterion of discovery of short abnormal waves with azimuth scan pulsed microwave radar.