Astrill is somewhat contradictory in this respect. It says that while it does not store any subscriber information or keep any logs, it does need to store some information for the technical functioning of services.
Information stored during the duration of your session includes connection time, IP address, device type and Astrill VPN application version. Astrill says this information is permanently deleted when the session ends, and is only used to check that you don’t exceed the limit on the  number of simultaneously connected devices.
Astrill also monitors the volume of web traffic generated by each subscriber, which it says is to inform any future network expansion. It also stores information about your last 20 connections for up to 30 days. This includes connection time, connection duration, country, and device type.