Why am i not able to delete any photos from my photo stream?

I have some old photos that are on my iPhone and will not allow me the option of deleting them. I also have a lot of pictures that were shared to me through an album my brother created after he had his baby and i am not able to delete them. It is very frustrating as i need more room on my phone for new photos! i just want the option of taking them off. Any suggestions?