Satoph

Satoph is a Het ship between Satoru and Toph Beifong in the Avatar: The Last Airbender series.

Canon
Toph and Satoru first met at the Earthen Fire Refinery. Satoru was immediately impressed by her feats that he accomplished during the war and the fact that she discovered a whole new sub-skill of earthbending. Toph, in turn, immediately seemed to develop a crush on him and said that it was nice to make an acquaintanceship with him. They then a made a deal between the refinery and Toph's metalbending school.

Toph had traveled to the refinery with Aang and he had a problem with the fact that it was on sacred Air Nomad ground. He claimed that it was Loban and Satoru's fault for the river becoming polluted and Toph quickly came to the defense of the refinery. She used her truth-seeing seismic sense ability and confirmed that Satoru was telling the truth. Aang accused Toph of being biased due to her crush on Satoru so Toph retorted that Aang was biased due to his cultural traditions.

Toph later saw Satoru's uncle Loban yell at him. Satoru just stood there and took it so Toph decided to butt in. Toph called him a "sniveling flunky" and said that it was just something that she does not respect. Satoru claimed that he was just trying to respect his uncle. Their relationship was strained by this disagreement and Satoru felt that Toph did not have the right to say what she said as he felt that she knew nothing of what he and Loban had been through.

Fanon
Satoph is a popular ship in the Avatar fandom. It had been many years since the series ended when The Rift trilogy came out and Toph still had no known love interest. It was revealed that Toph had a daughter with an unknown man and fans wanted answers as to who he could be. With a new love interest being introduced for Toph, many fans were excited and hopes that he would be Lin's father. However, Lin's father turned out to be a man named Kanto. Still, Toph also has a daughter named Su so some fans are hoping that Satoru is Su's father.