While needing to ensure the health and safety of their employees during the Covid-19 pandemic, employers face many burning data protection questions, including under what conditions they can process employees’ personal data (in particular health data) and whether gathering personal data concerning employees’ medical history, trips and contacts with infected persons, is allowed. This article focuses on issues that are problematic, based on the analysis of guidance issued by the European Data Protection Board, as well as national data protection authorities and practitioners from 20 countries in response to these concerns. The first section of the article analyses concepts of personal data and health data in the context of Covid-19. Then the article proceeds with exploring what possible legal bases employers can use to process employees’ personal data in general, and health data in particular, under the General Data Protection Regulation when applying different measures to combat Covid-19. In the latter part of the article two practical questions raised by employers – concerning the checking of employees’ body temperatures and informing them of possible infection – are discussed. The analysis indicates that national data protection authorities seem to look for a reasonable and pragmatic approach regarding compliance with the GDPR in light of the Covid-19 emergency. However, their guidance differs in several areas and the views in between nation states are not always aligned. A more specific, clear and uniform pan-European vision concerning the processing of employees’ data in times of emergency is needed to better protect employees and limit the spread of the virus.