Last three years has brought numerous challenges to educators at various levels, and in the same time dynamic progress in dissemination of the teaching technologies. These resulted in the increase in knowledge on the remote and hybrid teaching process yet revealed research gaps unrecognized before. The paper presents the research aiming to fill in the research gap by recognizing problems perceived by educators and emerging from online and hybrid teaching. The problems were recognized thanks to international-range research within HOTSUP project. The list includes infrastructural, technical, technological and methodological problems that were addressed in the further stages of the project.