[6] After splitting the 2012–13 season between Honeybaked and the USHL, Joshua was drafted 156th overall by the Plymouth Whalers in the Ontario Hockey League (OHL) Priority Selection.

[10] After drafting Joshua, Maple Leafs' amateur scouting director Dave Morrison spoke highly of him as a player, saying: "He's tall, very athletic and we saw some flashes of real good skill towards the end of the year.

[14] He helped the Buckeyes qualify for the 2016 Big Ten tournament, but they lost in the semifinals to the top-seeded University of Minnesota.

[15] The following season, Joshua recorded 12 goals and 23 assists,[1] earning Honorable Mention All-Big Ten accolades in March 2017.

[21] As a free agent from the Blues, Joshua signed a two-year, $1.65 million contract with the Vancouver Canucks on July 13, 2022.

[23] On June 27, 2024, after setting career-highs in goals and assists with the Canucks, Joshua signed a four-year, $13 million contract extension to remain with the team.

[24] In the summer of 2024, Joshua was diagnosed with testicular cancer, which required surgery and made him miss the training camp for the 2024–25 season.