Exim comes with a utility called ‘exiwhat’ which will display what each instance of exim is currently involved with. The output will look similar to this:
root@server [~]# exiwhat
2118 daemon: -q1h, listening for SMTP on port 25 (IPv4)
2130 daemon: no queue runs, listening for SMTPS on port 465 (IPv4)
31640 handling incoming connection from [1.2.3.4]
Also, to monitor the exim log in realtime, you may use the tail command thusly:
tail -f /var/log/exim_mainlg