To mitigate the negative effects of false information more effectively, the development of Artificial Intelligence (AI) systems to assist fact-checkers is needed. Nevertheless, the lack of focus on the needs of these stakeholders results in their limited acceptance and skepticism toward automating the whole fact-checking process. In this study, we conducted semi-structured in-depth interviews with Central European fact-checkers. Their activities and problems were analyzed using iterative content analysis. The most significant problems were validated with a survey of European fact-checkers, in which we collected 24 responses from 20 countries, i.e., 62% of active European signatories of the International Fact-Checking Network (IFCN). Our contributions include an in-depth examination of the variability of fact-checking work in non-English-speaking regions, which still remained largely uncovered. By aligning them with the knowledge from prior studies, we created conceptual models that help to understand the fact-checking processes. In addition, we mapped our findings on the fact-checkers' activities and needs to the relevant tasks for AI research, while providing a discussion on three AI tasks that were not covered by previous similar studies. The new opportunities identified for AI researchers and developers have implications for the focus of AI research in this domain.