You can look at the breakdown (sundurliðun) of your phone and internet history by signing into Stóllinn on nova.is. Just log in with your electronic ID and if you are registered as the user of that number then you can see the breakdown.

The breakdown only goes back 6 months and it gets deleted if the user of the number changes. It disappears as well if the SIM card is changed.

The breakdown only shows outgoing calls and SMS from that number as well as internet usage by hours. It does not show incoming or missed calls, you can only access that in the call history on your phone.

To see the breakdown, log into Stóllinn and click on the number you want to take a look at and choose "sundurliðun" on the navigation bar that appears as you can see here: