Bungie set hard mode live at around 1 p.m. ET; it requires a download. There are a number of Destiny items that players can't get anywhere outside of hard mode, such as weapons like the Word of Crota hand cannon and Oversoul Edict pulse rifle. And an item drop in hard mode is required to upgrade the Eidolon Ally auto rifle to the Necrochasm. Loot that's exclusive to Crota's End on hard includes a ship called "Bane of the Dark Gods" and a unique shader, Glowhoo.
A number of hardcore players from the Destiny community are livestreaming their attempts at tackling hard mode. You can follow along on the Destiny subreddit. For more on The Dark Below, the expansion that contains Crota's End, check out our full review.
Update: The world's first Crota kill on hard mode came less than two hours after Bungie set it live, the studio confirmed on Twitter. Five members of the clan One and Done, along with a sixth fireteam member, pulled off the feat. The group consisted of four level 32 Guardians and two level 31 Guardians.