RADICAL-Cybertools (RCT) are a set of software systems that serve as middleware to develop efficient and effective tools for scientific computing. Specifically, RCT enable executing many-task applications at extreme scale and on a variety of computing infrastructures. RCT are building blocks, designed to work as stand-alone systems, integrated among themselves or integrated with third-party systems. RCT enables innovative science in multiple domains, including but not limited to biophysics, climate science and particle physics, consuming hundreds of millions of core hours. This paper provides an overview of RCT systems, their impact, and the architectural principles and software engineering underlying RCT