As far as I am aware, they can obtain the following from the network provider very easily -
Number called, time of call and duration. We all know they can access voicemail.
Regarding messages the the network provider will have details of number sent and received, time and message size. Regarding text message contents it depends on a few factors such as the network provider (i know historically Virgin Mobile kept copies, so others may do the same), whether the phone has ever been backed up or connected to say a Gmail account. I would not be surprised if armed with a court order, IMEI, some nifty software and a few civilian graduate uber geeks (which most of the techie ones are in the labs) it is possible. I will ask the question next time I’m onsite at a lab.
Also, I may be wrong on this, but there is always a buzz of excitement in the labs if the phones are on contract rather than PAYG.
I know with Whatsapp messages they deactivate the lost sim, obtain a new sim card with the same number and do a bit of jiggery pokery and whatsapp is reinstated with all messages, photos and call logs intact.