Terminator: Genisys (2015)
Genisys begins with Kyle (Jai Courtney) and John (Jason Clarke) carrying out their final attack on Skynet, just as the original films described. All goes according to plan until Kyle steps into the Time Displacement Device; a moment John says is the actual end of the war, and the closing of the series' time loop. Moments before departing, Kyle witnesses a T-5000 (Matt Smith) grab hold of John, and leave his fate unknown.
The film later reveals the T-5000 to be Skynet in physical form, having killed all soldiers present and infected John, triggering a replacement of his entire physiology with phased machine matter (essentially turning John into a Terminator, referred to as the T-3000). The T-5000's fate is unknown, but he uses the Time Displacement Device to send John to the year 2014 in the film's new, Judgment-Day-less alternate timeline.
Upon arriving in 1984, the deployed Kyle and the T-800 follow the paths they walked in the original Terminator, until an aging T-800 ("Pops") appears to kill the newly-arrived machine with the help of Sarah Connor (Emilia Clarke). Elsewhere, Kyle is pursued not only by an L.A.P.D. officer, but a T-1000 in disguise. The duo of Pops and Sarah save the day, with the would-be damsel in distress informing Kyle that Pops has been training her for war since the age of 9, when a T-1000 killed Sarah's parents, and Pops miraculously appeared to act as her guardian.
Claiming that the version of the past John sent Kyle into no longer exists, the team defeats both enemy Terminators, and use their own Time Displacement Device to travel forward in time to stop Judgment Day. For Sarah and Pops that date is August, 1997, but Kyle recalls memories of an alternate future - his alternate past - in this new timeline, in which Judgment Day occurred in October 2017, triggered by a project known as Genisys.
Pops theorizes that because Kyle was displaced from time during John Connor's death - a major event in the flow of time, given his role in the destiny of the world - he is able to glimpse two futures: that which he learned of growing up in the ashes of the old world, and the normal life he would have had in this new, Judgment-Day-less timeline. Sarah agrees, and the pair depart for 2017.
Upon their arrival, Kyle and Sarah are visited by John (the T-3000), having spent the last three years in this timeline creating the Genisys operating system with Cyberdyne's Danny Dyson (Dayo Okeniyi), son of Miles Dyson. Kyle, Sarah and Pops set out to destroy Genisys before the OS launches, linking a billion people's personal electronic devices and - yet again - getting its hooks into the military's weaponry ("Genisys is Skynet," after all).
As John battles Pops, Sarah and Kyle meet Skynet years before it is able to take a human form as the T-5000, managing to destroy the complex and John along with it, with Pops enjoying some "upgrades" courtesy of a dip in the liquid metal baths used to create the T-1000s. Assuming Skynet has once again been stopped, Kyle gives his younger self the memories needed to save the day (12 years in this other future), and all set off to make their own fate. That is, until a credits scene reveals Skynet to be intact, with the formless T-5000 admiring a massive red power core.
The practical problems should be evident to any fan upon seeing Genisys, the main issue being Kyle Reese's travel from the future established in the original series, to a past that would clearly not produce that same future. Kyle mentioned to Sarah in The Terminator that the time he came from was just "one possible future" - though that wasn't his field of expertise - but basic assumptions of time travel would state no matter how he does it, the Kyle Reese 0f 2029 could only travel back along the timeline which produced that future.
The only real explanation is that "access point" created by the death of John Connor (which granted Kyle memories of both timelines) also allowed him to leap from one to the other. It's a leap that is unexplained for now, but the actual means by which Kyle changes timelines, like the question of who sent back Pops to protect Sarah, will form the plot of this new Terminator film series.
And the secret likely rests in the T-5000.