For over 70 years, ferroelectric materials have been one of the central research topics for condensed matter physics and material science, an interest driven both by fundamental science and applications. However, ferroelectric surfaces, the key component of ferroelectric films and nanostructures, still present a significant theoretical and even conceptual challenge. Indeed, stability of ferroelectric phase per se necessitates screening of polarization charge. At surfaces, this can lead to coupling between ferroelectric and semiconducting properties of material, or with surface (electro) chemistry, going well beyond classical models applicable for ferroelectric interfaces. In this review, we summarize recent studies of surface-screening phenomena in ferroelectrics. We provide a brief overview of the historical understanding of the physics of ferroelectric surfaces, and existing theoretical models that both introduce screening mechanisms and explore the relationship between screening and relevant aspects of ferroelectric functionalities starting from phase stability itself. Given that the majority of ferroelectrics exist in multiple-domain states, we focus on local studies of screening phenomena using scanning probe microscopy techniques. We discuss recent studies of static and dynamic phenomena on ferroelectric surfaces, as well as phenomena observed under lateral transport, light, chemical, and pressure stimuli. We also note that the need for ionic screening renders polarization switching a coupled physical-electrochemical process and discuss the non-trivial phenomena such as chaotic behavior during domain switching that stem from this.