The corporation based out of the Oscorp Tower in New York. It was created and run by its CEONorman Osborn. Norman studied chemistry and electrical engineering in college. He also took a number of courses in business administration. Norman Osborn's teacher, Professor Mendel Stromm, formed the business partnership. Since Norman put up the bulk of the financing, they called their company the Osborn Corporation, or Oscorp.
Dr. Nels Van Adder, a research assistant, helped Dr. Stromm at Oscorp developed a performance enhancing formula which would later be known as the “Goblin Formula”. Later on this proved to be another failure for Oscorp as Norman Osborn died which left his son Harry to run the company. Since then there hasn't been one update on any projects that could help man-kind. But there have been rumors that there still are experiments going on in the locked up basement of Oscorp to date. While Harry Osborn hasn't been seen in months, there has been speculation that he could have been an Oscorp guinea pig and that he had been killed. There also have been rumors that Spider-Man has been linked into the problems somehow given that he has strange super human powers.
Mendel Stromm's early research was on a chemical that would provide enhanced strength in its test subjects and would eventually turn Osborn into the Green Goblin. Osborn, wanting the formula for himself, discovered that Stromm had been embezzling funds from Oscorp. Stromm explained that he was merely borrowing but Osborn turned him over to the police. After several years in prison, Stromm was released and tried to kill Osborn for revenge using evil robots. He was stopped by Spider-Man and seemingly died of a heart attack when he was nearly shot.
The company was created after Jay Allan's company "Allan Chemical" was merged with her son's Normie Osborn's stocks from Oscorp and the last remaining properties of Horizon Labs after its destruction, establishing it under the new name of "Alchemax".
It was later revealed that Norman Osborn, under the guise of "Mason Banks," created the corporation in order to leave a strong empire for his grandson and establish an empire for the Osborn legacy. Their headquarters, Oscorp Tower, was the former headquarters of Oscorp.
By 2099 Alchemax would eventually control most aspects of daily life in a possible future.
After an incident in which Osborn injected himself with Oz serum, a big portion of the main building was left in ruins, and numerous scientist died  Osborn Industries had been mentioned to still produce technologies.
In other media
Oscorp is featured in the Spider-Man (1994 TV series). Norman Osborn hires Spencer Smythe to create a weapon to destroy Spider-Man by creating the Spider-Slayer. The deal made with Osborn meant that Norman would build a hoverchair for Spencer's paralyzed son, Alistair. The Slayer unintentionally captured Flash Thompson dressed as Spider-Man, and the real Spider-Man came to his rescue. his led to a large scale fire in the Oscorp plant. Norman Osborn quoted to Spencer "Remember our deal. No Spider-Splat, No Hoverchair." Spencer chose to stay behind and finish Spider-Man off while Norman got Alistair to safety. After the Spider-Slayer was destroyed by Spider-Man, Oscorp exploded and Spencer supposedly perished. However, Spencer had survived, having been found by the Kingpin. Norman invented the technology which would create the Hobgoblin and hired him to assassinate Kingpin. The assassination was foiled by Peter Parker and the Kingpin suspected a conspiracy against him. Norman subsequently fired the Hobgoblin, who allied with Kingpin and kidnapped Norman's son Harry. When the Kingpin refused to pay Hobgoblin immediately, they ceased their partnership. Following this, Osborn sold 50% of his company to the Kingpin in order to repay his debt. Norman and his partner Wardell Stromm were forced into creating chemical weapons for the Kingpin. An unstable reaction resulted during one experiment and Norman seemed to have perished in the explosion. However, Norman had survived the explosion, his strength enhanced by the gas from the explosion, and this combined with the Hobgoblin weapons created the Green Goblin. He then began kidnapping the Oscorp stockholders, although Spider-Man uncovered an underwater base where the Goblin intended to kill them. Fighting the Goblin, Spider-Man unmasked him. Amnesia ensued and Norman was unable to remember his dual identity. The following morning, Norman publicly announced that Oscorp would no longer be involved in the creation of chemical weapon.
Oscorp is featured in the The Spectacular Spider-Man. Bent on being the number one in weapons tech, Norman embezzled the designs of Adrian Toomes and then tipped Big Man on the technology created by Tri-corp on shipment. As a result, Norman considers Big Man's deal, with him receiving guinea pigs for his illegal experiments in return for the created supervillains to distract Spider-Man from Big Man's operations. Bent on finding out the truth after learning the "Globulin Green" vial is missing and tied to his "benefactor", Norman tells Hammerhead he is determined to unmask the Goblin at any cost. It is eventually revealed that Norman Osborn was actually the Green Goblin throughout the series.
Oscorp is featured in The Amazing Spider-Man. When Oscorp scientist Dr. Curt Connors used lizard DNA to try and regrow his missing arm, the serum took over, turning him into a giant lizard whenever he injected himself with the serum. He tried to use a piece of equipment called the Ganali Device to spread this serum all over New York, turning everyone it touched into lizards just like himself. Luckily, he was stopped by Spider-Man before he could spread the serum across the city. It was also mentioned that Norman Osborn was dying from a disease.
In The Amazing Spider-Man 2, Oscorp electrical engineer Max Dillon was repairing a large cable when it suddenly electrocuted him. He fell through several platforms into a tank full of genetically altered electric eels. They shocked him multiple times until the tank shattered. Max emerged with blue, glowing skin—he had been turned into a living electrical capacitor. Dubbing himself Electro, he stumbled out of Oscorp into the streets. Harry Osborn becomes its CEO after his father's death. Accessing Oscorp's Secret Projects lab, Harry assumes the mantle of the Green Goblin.
The Oscorp building from The Amazing Spider-Man almost appeared in The Avengers. However, by the time the Oscorp building was fully designed for Spider-Man, the Avengers skyline was rendered, so for timing the idea was abandoned.
Oscorp appears in the 2002 Spider-Man. The company in the game parallels that of the film, with Norman Osborn and his scientists attempting to capture Spider-Man in order to study his genetics to perfect their own contracted super-soldier serum. After a number of failed attempts to capture Spider-Man using Oscorp robots, Norman subjects himself to the serum and becomes the Green Goblin.