LUKS can't encrypt the /boot partition, but everything else including your root partition can. That means GRUB and your kernel won't be encrypted, but everything else, including your files, programs, and logs, will.
This is similar to how TrueCrypt works. It has its own unencrypted bootloader that decrypts and runs Windows.
Many distributions allow you to encrypt entire partitions during installation. Fedora does using the normal installer, just check Encrypt this filesystem in the partitioning setup. Ubuntu also permits you to encrypt whole partitions, but you must use their alternate install media to do so. Live media only supports home directory encryption.