Short answers, pulled from the story.
The very first motion pictures created by Thomas Edison lasted only 46 seconds. This duration was dictated by the physical limitations of film reels rather than artistic choice. In 1894, the Kinetoscope device could only hold enough film for a fleeting glimpse of reality.
Major studios began to dismantle their short-subject production lines in 1938. Hal Roach discontinued all short-subject production except for the Our Gang series that same year. The Vitaphone studio and Educational Pictures also ceased their lines of two-reel comedies in 1938.
The last live-action two-reel comedies ended production in 1959. The Three Stooges were the final group to continue making these films before the medium shifted to student and independent work. Most studios canceled their live-action series in 1956 as television rose to prominence.
Warner Bros. produced the last regular theatrical cartoon short series known as The Pink Panther. This series began in 1964 and ended in 1980. It spent its entire existence in the limited animation era before shifting to television syndication.
Pixar started screening a short film with each of its feature films during its initial theatrical run in 1995. The studio has been producing shorts permanently since 2001. Disney acquired Pixar in 2006 and began producing animated shorts in 2007.
Tropfest originated in 1993 and claims to be the world's largest short film festival. It has expanded to Australia, Arabia, and the US. This festival is often credited with driving the recent international popularity of the short film form.