Microservices are gaining tremendous traction in industry and a growing scientific interest in academia. More and more companies are adopting this architectural style for modernizing their products and taking advantage of its promised benefits (e.g., agility, scalability). Unfortunately, the process of moving towards a microservice-based architecture is anything but easy, as there are plenty of challenges to address from both technical and organizational perspectives. In this paper we report about an empirical study on migration practices towards the adoption of microservices in industry. Specifically, we designed and conducted a survey targeting practitioners involved in the process of migrating their applications and we collected information (by means of interviews and questionnaires) on (i) the performed activities, and (ii) the challenges faced during the migration. Our findings benefit both (i) researchers by highlighting future directions for industryrelevant problems and (ii) practitioners by providing a reference framework for their (future) migrations towards microservices.