(written from a Production point of view)
The Orville is a live action parody and homage to Star Trek, specifically Star Trek: The Next Generation. The show is created by, and starring Seth MacFarlane and is co-produced by Brannon Braga, former Family Guy collaborator David A. Goodman, alongside another Star Trek veteran Andre Bormanis, who reprised his role as technical advisor. Braga himself states the series "is aiming to tell stories that ride the line between drama and comedy, with an eye toward earnestness." 
Set in the 25th century, the series chronicles the adventures of The Orville, a mid-level starship exploring the galaxy on behalf of the Planetary Union. Her captain is Ed Mercer, who receives the job due to no other captains being available, his career having slumped after a divorce. Mercer's hope of proving himself and serving the Union are complicated when his ex-wife, Commander Kelly Grayson, is assigned as his first officer. Despite initial tensions with Kelly, Ed soon forms a tight-knit crew.
The series was officially announced in March 2016, though MacFarlane had stated for years he had a passion for science fiction and space opera related media. He was reported to have heavily managed every detail of the series during the show's productions, wanting The Orville to truly be a thriving universe that could justifiably be seen as a spiritual successor to the Star Trek series before it. MacFarlane had also expressed inspiration from not just Star Trek, but the Twilight Zone, Marvel's Guardians of the Galaxy, and Deadpool as well.  
The Orville debuted in September 2017 for FOX TV and starring MacFarlane as Captain Ed Mercer, with Penny Johnson Jerald as chief medical officer Claire Finn, and Scott Grimes as helmsman Gordon Malloy. Star Trek actors appearing in the series have, so far, included Victor Garber, Brian George, J.D. Cullum, James Horan, Ron Canada, Joel Swetow, Brian Thompson, Molly Hagan, Steven Culp, Michael Duisenberg, Jason Alexander, John Fleck, Tim Russ, F. Murray Abraham, Tony Todd, Marina Sirtis, Robert Picardo, and John Billingsley (with Picardo and Billingsley appearing together in the episode "Home"); MacFarlane, Braga, James L. Conway, Jonathan Frakes, and Robert Duncan McNeill have directed episodes. Marvin V. Rush – who was director of photography for TNG, serves as the show's cinematographer.
Although initially promoted as a spoof, the series is in fact a comedy-drama (dramedy) done in the style of TNG. MacFarlane had previously expressed interest in rebooting the Star Trek franchise in October of 2011, when he mentioned to the Hollywood Reporter that he was eager to reboot a Star Trek series for television: "I'd love to see that franchise revived for television in the way that it was in the 1990s: very thoughtful, smartly written stories that transcend the science fiction audience. I don't know who would give me the keys to that car."  MacFarlane indicated his intent was to pay homage to Star Trek with the show while resurrecting the style of optimistic science fiction TNG espoused.  In this MacFarlane succeeded eventually, as his show not only attracted "Trekkies" disenchanted with Discovery for canon and philosophical premise reasons (and reminiscent of how Ronald D. Moore's re-imagined Battlestar Galactica drew in Star Trek fans who were disenchanted for basically the same reasons with Star Trek: Enterprise over a decade earlier), but also former Star Trek production/franchise staffers like Michael Okuda and Larry Nemecek. 
A major difference with its contemporaries became the decision to go "old school" with a traditional physical studio model for the establishing shots of the "hero ship" Orville in order to get the retro feel MacFarlane was aiming for. By that time a near obsolete visual effects (VFX) technique in the age of CGI, pilot episode Director Jon Favreau contracted several veterans still versed in the antiquated technique which included Star Trek alumnus and veteran Robert Legato for the motion control photography. Even though the majority of the other visual effects shots were executed as CGI, the footage taken of the physical model served as a library of stock footage (especially for the show's intro), apart from the model being used as as scanning model as well as a camera test model.  The creation of a stock footage library had actually already been Legato's original intent to begin with for the two original USS Enterprise-D physical models for The Next Generation back in 1987. (Star Trek: The Next Generation Companion, 3rd ed., p. 31)
Due to Star Trek: Discovery's production delays, The Orville ended up debuting only two weeks before Discovery, leading to many reviewers making head-to-head comparisons between the shows.
The first season, consisting of 12 episodes, concluded in December 2017. A second season was commissioned soon after its debut (along with Star Trek: Discovery, The Orville was one of the first new series of the 2017-18 season to be renewed). Prior to broadcast of Season 2, MacFarlane indicted that the second season would have a more serious tone than the first, downplaying comedy in favor of more straightforward science fiction storytelling. Season 2 debuted at the end of December 2018 and scheduled the same night as new episodes of Discovery were released on CBS All-Access, which strengthened the perceived impression of the two having become de facto franchises contenders. This was reinforced by the 2019 Emmy Award nominations where The Orville's second season was put up against that of Discovery for the most coveted technical category, that of "Outstanding Special Visual Effects"  – though neither of them won the coveted prize as it went to the wildly popular Game of Thrones, former Star Trek VFX staffer Joe Bauer being one of the recipients.  An ironic circumstance was that The Orville was from its second season onward served by digital VFX vendor Pixomondo, Discovery's primary CGI vendor from its very inception.