This study focused on the specific challenges of university students in the face of the COVID-19 pandemic and examined similarities and differences in COVID-related concerns and difficulties in functioning in samples of undergraduate students in five countries. A sample of 4306 undergraduate university students (43.8% males, 56.2% females) from Israel, Kosovo, Ukraine, Cyprus and Germany participated in an anonymous online survey during the first wave of the pandemic, between March and June 2020. Study variables included the assessment of the exposure to COVID-19, perceived health status, specific COVID-related concerns and functional difficulties, social support, and the perceived level of coping. Similar concerns about the uncertainty regarding the termination of the health crisis and worry for the health of family members were identified as the most common concerns in the five countries. Challenges in online learning and financial difficulties were rated as the most central difficulties. Both COVID-related concerns and COVID-related difficulties predicted lower levels of perceived coping. Greater social support was associated with better perceived coping. Policymakers should be informed by the accumulating research showing the substantive relationships between academic difficulties and perceived COVID-related distress and coping.