The latest advancement in the 3DS homebrew scene is here: SigHax, and Boot9Strap. Thanks to the 3DS's bootroms being dumped, SigHax/B9S allows for CFW to be run instantly after the execution of the bootrom. This opens many doors for homebrew developers, and the scene in general.
Here is an early FAQ for users that want to know more information on what exactly SigHax is.
Thanks to @icefire82G
Of course, if you need to know anything in intricate detail, the 3DS guide has you covered.
If you're wary of the chances of bricking your 3DS, check this user-updated poll, which keeps track of successes and bricks.
Thanks to @LiaLuma3DS (with SigHax support)
All future releases of Luma3DS will only be made in the .firm format, which will only be compatible with boot9strap and sighax. This means that to continue receiving the latest updates of Luma3DS, you should use this page to update your installation.
If you have any corrections to offer, please PM them to me, and I will update the OP to the best of my ability.