The article explored the modern global educational space and university environment with its structure and functioning. It presents key tasks of US university education in a global context, offers the definition of the university environment, and describes core features of the US university setting. The university campus is considered as a main educational space for students to live and study. It has been given the description of the structure, main functions and services of a university campus needed to facilitate students' learning process. Pedagogical support for fostering a welcoming and effective learning environment has been outlined, too. It also lists diverse students' main challenges in an unknown university setting, which they primarily met with; the theoretical findings were justified by the recent research results. The core student competences were studied that are extremely important to be acquired and developed in order to overcome adjustment and studying challenges. The article has explored some primary tasks of the university staff, primarily, international student counselors and educational counselors, who work with students of different cultural backgrounds, aiming at helping them with their adjustment and studying problems.