The last episode of Dragon Ball Super, not a lot was revealed about the mysterious villain, Black. The episode starts where the last one left off, in the future, with Trunks holding Mai's lifeless body in front of Black. Black, then said it was "[Trunks'] turn," and started provoking Trunks to attack by insulting his strength as a warrior and the Saiyan race in general. What was weird was that he was talking about Saiyans as if he himself were not also a Saiyan, which should lead us to believe that Goku has lost control of his body somehow, but that is all we know for sure. However, there are rumors that Black may be a fusion between Goku and a Makaioshin. A Makaioshin is a demon world version of the Supreme Kais, that rule over all of demon world. They also possess the same power of a Grand Supreme Kai. It actually makes a lot of sense, and explains the green potara earring and new body that Goku has. However, the result of the fusion is not consistent with potara earring fusion rules. If it followed these rules, Black would still have at least some of Goku's personality in him, but there is no sign of Goku's personality, seeing as Black is pure evil and cannot sense ki as well as Goku normally can. But, considering the fact that we have never seen a green potara earring, there may be new rules for this fusion that would explain why Black seems to be completely controlled by the Makaioshin.
Back to the recap: After Black succeeds in provoking Trunks to power up and attack, Trunks gets one good punch in, but that would be the only hit he gets on Black. The fight becomes one-sided very quickly and Trunks becomes badly wounded, but he is able to escape, because, like almost every other super villain before him, Black drags his feet on killing him and makes it into a huge theatrical scene. This gave Trunks enough time to find his sword amidst the rubble of a destroyed building and throw it, boomerang style, at Black's hand to stop him from attacking, and then proceeded to fire a decoy ki blast that allowed him to escape. Then, in dramatic fashion, Trunks is able to escape to the past just as Black fires another, surely life ending, ki blast. Trunks then passes out on the dash board of the Capsule Corp. time machine.
The scenes in the present start with Trunks, Pilaf, Mai, and Shu in math class. The teacher asks Trunks to answer the problem on the board, "1000 - 900 x 0.5=." Trunks mistakingly subtracts before multiplying, and Pilaf jumps up, in very Pilafesque fashion and does a whole song and dance explaining PEMDAS (honestly while watching this scene I did the same thing, and immediately blurted out "50!" in my head, and felt so dumb when I had to watch Pilaf explain why I was wrong, in a grandiose and cartoonish musical number). Everyone applauds Pilaf after his explanation, further inflating his ego, and the class ends. After class they start walking to lunch, and we see another cute/romantic moment between Mai and Trunks, which, to be honest was pretty cool to see.
Before they were able to get to lunch Future Trunks crash lands in the present outside of Capsule Corp. and they go to investigate. When the get out side Trunks flies up to the time machine, and the teacher freaks out, because she does not know that Trunks is a Saiyan or even what a Saiyan is. I though that was great, because so often the Z-Fighters get so caught up in their own adventures that we forget that they are still on Earth with humans that do not know they are aliens. But anyways, Trunks looks through the glass of the time machine and sees an injured person, and Pilaf tells Shu to run and get Bulma. They eventually get Future Trunks laid out on a bed, and Present Trunks had a chance to look at his future self. Pilaf, Shu, and Mai start speculating as to who he was. The best theory they could come up with was that Future Trunks was the illegitimate son of Vegeta and that Trunks had a brother. Bulma, on the other hand is trying to contact Goku and Vegeta, who are, of course, with Whis and Beerus training. Interested in the peculiar situation, Whis and Beerus decide to go back to Earth with Goku and Vegeta. When they get back they are able to give Future Trunks a senzu bean, and he regains consciousness. But when he sees Goku's face Trunks remembers how Black murdered Bulma and Mai, then gets up and tries to attack Goku, and the episode ends with everyone completely confused and surprised.