Chapter 82 of "Boko no Hero Academia" is already online courtesy of D-Manga. The current chapter continues the story arc where the heroes in training and their teachers are under attack by villains with the purpose of kidnapping Katsuki. Before any predictions and speculations of the upcoming chapters, here's a brief recap.
At the facility, Blood King orders the students to stand their ground despite their please to fight outside. Out of nowhere, Dabi attacks the facility and the students were saved by Blood King just in time. Dabi informed them of their objective: to kidnap Katsuki as well as to disrupt the school's reputation most especially the heroes who run them. Shouta appears with Kouta and informs Blood King that it's just a mere clone and they should move ahead. Blood king was put in charge of the facility while Shouta looks for other heroes and students.
On the other hand, Shouto Izuku and Mezou caught up with the villains. However, they were unable to handle the various attacks of the villains. They were able to get a slight upper hand when Yuuga activates his navel laser.
However, they were tricked: even though Mezou was able to obtain the marbles from The Magician, those are merely decoys. They were able to grab hold of one of the marbles that contains Fumikage but unable to save Katsuki.
User ShenGao from Manga Helpers has posted a brief plot of the upcoming chapter. The attack has ended and even though no one was killed, Ragdoll and Katsuki are missing. Izuku wakes up at the school hospital with the rest of the gang around him.
User GrimTwin on Reddit also speculates that the upcoming chapter will be a briefer on what happened to the teachers and students, "we'll get a wrap up of how everyone is doing on the heroes' side first. Finding out if the Tora and Mandalay are okay, if Ragdoll is dead or not, all the students back together..."
