He was formerly the protégé of Professor Reynolds and a friend of Arthur Nielsen. In college, he conducted experiments with teleportation, using Rheticus' Compass, having deciphered almost all of the instructions encoded on the device. He attempted to use the Compass before finding all of the instructions, however, and was believed dead after activating the device.
Claudia and Artie later discovered that Joshua was, in fact, not dead, but suspended in some sort of interdimensional limbo. They managed to recreate the conditions of Joshua's experiment, finding him with the Compass in the immaterial interspace, and carrying out the final instruction necessary to bring Josh back to the corporeal realm.
After returning to the material world, Joshua initially did very little, loafing idly at Leena's Bed and Breakfast. Artie found him a job at the particle physics laboratory at the European Organization for Nuclear Research, where he had access to antimatter.
James MacPherson exploited Joshua's position to acquire a sample of antimatter, throwing Joshua over a railing in his escape from the facility. Josh survived the fall, and was reunited with Artie and his sister.
Whilst frequently referenced, by Claudia and other characters, he is relatively little seen, and, in the third season, is arguably "supplanted" on a day-to-day basis in Claudia's life by Steve Jinks, who himself notes the tremendous similiarities between Claudia and his own sister, whose death motivated him to become an ATF agent.
Joshua reappears in "The Ones You Love", encased in a shell of amber from Pliny the Elder's Scroll, sent to him by Artie while under the effects of the Astrolabe. After Claudia frees him, he asks how she managed to find him, explaining that he had moved in secret and only informed Artie, leading Claudia to understand that Artie was the only one who could have sent the artifact to Joshua.