Nowadays situation at the universities in Ukraine and all other countries round the world are faceted with different challenges almost every new quarter of the year. The very vivid example of it was the pandemic period, which determined transforming of forms of education and different approaches to education. Moreover, the Pandemia provoke the huge wave of challenges for scientific and pedagogical staff of universities. A great number of changes took place at the system of educational process organization: pandemic has exacerbated the need for digital, technology-enabled education experiences, new types of online-classes appared and new ways to scale them etc. But after pandemic period and all these transmitions in universities their appared the need for analyses of challenges which we are going to face with, when we come back to ordinary style of teaching? what problems are we going to solve? To answer these questions, we created a Questionnaire for teaching staff and students of different Universities in Ukraine in different regions. We asked them to give their feedbacks, opinions and feelings of the quarantine restrictions of COVID-19, what difficulties they had durining the next few months. The investigation helped to distinguish challenges to scientific and pedagogical staff of higher educational institutions, the nature of which is the peculiarities of the professional activities of teachers and challenges to the scientific and pedagogical staff of higher educational institutions, the nature of which are the features of the educational activities of students.