It is well-known that the 10-dimensional superstring effective actions contain an infinite series of alpha' corrections that introduce higher-derivative terms in the equations of motion. These corrections have important implications for black holes, and they are necessary in order to compare the black hole entropy with the microscopic one when the number of branes is finite. Despite of their interest, so far the study of alpha' corrections to black holes has been almost entirely focused on near-horizon geometries. \par In this talk I will present an explicit family of global, supersymmetric black hole solutions that contain all the first-order in alpha' corrections, and I will extract some intriguing conclusions. \par By interpreting the solution as a background of stringy objects, we will compare the corrected black hole entropy with the microscopic one, and we will see that there exists a tension with previous results. In addition, I will describe an special type of solutions known as ``fake small black holes''. These look like ``small'' black holes (those sourced only by a string and which are singular in the supergravity limit) but they actually are ``large'' black holes. I will argue that the small black holes constructed in the literature are indeed ``fake'' small black holes, and that the resolution of the horizon which was reported in previous studies is an illusion caused by the misidentification of the quantum numbers of the system.