In this article, a review of polarimetric synthetic aperture radar (SAR) methods for sea oil slick observation is presented. Marine oil pollution monitoring is a topic of great applicative and scientific relevance. In this framework, the use of remotely sensed measurements is of special interest and, in particular, the SAR because of its almost all-weather and all-day imaging capability at fine spatial resolution is the most effective tool. Conventional single-polarization SAR oil spill monitoring techniques are limited in their capability to detect oil slicks since they strongly rely on suitable thresholds, training samples, and ancillary information. Hence, an expert image analyst is due. The launch of a number of polarimetric SAR missions, along with the understanding of the peculiar physical mechanisms governing the scattering by an oil slick, led to a new paradigm (known as physical processing) that fostered a set of polarimetric algorithms particularly robust and efficient. Hence, suitable polarimetric models that exploit the departure from the slick-free sea Bragg scattering have been developed to effectively address oil slick monitoring. A set of polarimetric features extracted following such electromagnetic models have been proved to be reliable for oil slick monitoring. Polarimetric SAR observations led to a significant improvement in sea oil slick observation since they allow distinguishing oil slicks from a broad class of lookalikes in an unsupervised way. In addition, deeper information on the damping properties of the pollutant can be also inferred, which is of paramount importance for remediation purposes. Such physical processing has been demonstrated to be robust at variance of microwave carrier frequency, e.g. L-, C-, and X-band, and suitable to be exploited to extract information by dual-polarized, full-polarized, and compact modes. All these make such a physical approach of operational interest since it is able to exploit a larger set of SAR measurements building up a virtual constellation. In this review all these are detailed.