The focus of this talk will be on random matrices with square-integrable i.i.d. cooefficients, also known as Girko matrices. It is known, by a series of works that begins with Girko (1984) and ends with Tao and Vu (2010), that the empirical measures of properly normalized Girko matrices converge to the uniform measure on the unit disk. The question of the existence of outliers naturally appears. I will show, by a study of the characteristic polynomial of Girko matrices, that this question can be answered negatively. This talk is based on a joint work with Charles Bordenave and Djalil Chafaï [arXiv:2012.05602].