Samsung already started last week with June updates for the Galaxy S4 Exynos (GT-I9500) variant. Today Samsung started the updates for the Galaxy S4 Snapdragon (GT-I9505) variant. The updates are quite small but are specially for bug fixes and battery improvements. You could update your Galaxy S4 by Samsung KIES or OTA (over the air). Of course are all firmwares downloadable thought our firmware page.
Below a list which country has received the June Update.