You can delete a call or text from your history by pressing on the call in the history log and holding it. You'll then get a list of options, including the delete option.
I hope that helps, and welcome to AF!
Calllog - Phone app / press Menu, select Delete
SMS - Messaging / press menu and select "Delete all threads"
That depends on whether you want to delete the entire history or specific messages.
I assumed you wanted individual messages/calls deleted, which was probably not a good assumption on my part.
kejlyCZ brings up a good suggestion if you want to delete the entire history for SMS or calls.
Whichever situation you need, there you go.
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