Over the last 11 years, the field of Memristive Sensors abruptly emerged in literature. The present review paper has the aim to acknowledge such an exciting new field of research as well as to critically review its most significant outcomes. As usual in science and technology, only the concept of a new sensor has been drawn and simulated in some cases, while real demonstrators have been designed, fabricated, and demonstrated in several other cases. Moreover, several new sensing methods have been proposed, all based on memristive conductivity. Again, the new sensing principle has been shown just once in some cases, while several different sensors have been demonstrated by applying a single consolidated method in other cases. Therefore, ultimate aim of this paper is to deeply and exhaustive review the most important steps in such a new field by entering the significant details about the several kinds of sensor, while critically commenting on the key aspects of the proposed ideas and applications. The most important milestones are outlined as appeared along the course of the last decade, by also showing the temporal perspective of this totally new recently emerged field.