The PS3 allowed the ability to copy/paste text when composing or replying to messages.
Where is this function on the PS4?
In the on-screen keyboard, there should be a "..." button right below the space bar. Press that, then hit "Select" to start selecting the text you want to copy. Once you've finished selecting the text (using D-pad or thumbstick), press the X button to finish. Select "Copy" from the prompt that appears, and your text will now be copied. To paste text, use the same "..." button below the spacebar, then select "Paste" from the menu that appears.
The method mentioned above only works for text in an editable textbox, however. Only the PS Messages mobile app seems to allow copying/pasting text of a message that was already sent.
The PS3 version for a copy and paste was a lot more simpler to do. Because all you had to do was hold down the x button and slide it over the word that you were trying to copy in the internet browser and then notification come up asking you " Copy or paste". But for the PS4 version for some reason they have changed that functions, that you have to type in the word that you see in the internet browser by pressing triangle on your control pad to bring up the keyboard then going down to the three dots on below the spacebar and select that to copy the word that you have manually type in to copy which is redundant in my opinion.