In systemd based systems you use the application journalctl for that.
https://wiki.archlinux.org/index.php/Systemd/Journal#Filtering_output
For example this will show all the messages since the most recent boot:
sudo journalctl -b
This will show you any errors since the last boot:
sudo journalctl -b -p err
This will run a continuous output similar to what tail -F /var/log/messages would do:
sudo journalctl -f
It takes a little getting used to but it works well once you get accustomed to it.