Abstract. Currently optically pumped mirrorless lasing is represented by three distinct branches, which concern lasing in different types of the gain media: optically random and photonic media, and microcavities. This article is a first part of our review on optically pumped mirrorless lasing, with the random lasing in scattering media being a main subject. The other mirrorless lasing mechanisms will be addressed in the second part. Considering light localization as a key function of the feedback, we discuss possible mechanisms for the light localization in the scattering media. Special attention is paid to the Anderson light localization. The other mechanisms of the light localization in the scattering media concern high Q-resonances in local microresonators, which exist due to structural inhomogeneities in the scattered media. Applications of the random lasers are shortly reviewed.