The Search For Spock

Following the defeat of Khan Noonien Singh (see Star Trek II: The Wrath of Khan), the USS Enterprise limps back to Earth, heavily damaged from the battle. Once there, Admiral James T. Kirk is informed that the obsolete vessel's days are over (it is stated to be 20 years old, but official production timelines place it as about 40 years old, with Kirk's command of the Enterprise being about 20 years); it won't be refitted, but will instead be retired, and its crew reassigned. Meanwhile, Dr. Leonard McCoy exhibits strange behavior, somehow related to the deceased Captain Spock. He even seems to be channeling both Spock's behavior and voice. 
Simultaneously, Kirk's son Dr. David Marcus and Lieutenant Saavik are now on board the research vessel USS Grissom under the command of Captain J. T. Esteban to explore the Genesis Planet, created when Khan detonated the Genesis Device. While conducting sensor studies of the planet, Saavik detects an unidentifiable life form. Dr. Marcus asks Saavik to conduct a close range scan of the area and they discover Spock's burial tube. Dr. Marcus speculates that Spock's burial tube must have soft landed because of fluctuations in the gravitational field of the Genesis planet during formation. After a request to beam the life form on board is denied, Captain Esteban permits Saavik and David to transport down to the planet's surface to investigate the sensor readings. While there, they discover, much to their shock, that Spock's body has been resurrected by the Genesis effect, although his mind is no longer present and he operates on a purely child-like level. Marcus, pressed by Saavik, admits that he used unstable "proto-matter" in building the Genesis device to solve "certain problems". Without it, he claims that the Genesis Project could have been delayed by years or would have never been completed at all. The unstable matter puts the planet in a state of accelerated evolution that will conclude with its premature destruction within a few hours. 
Unknown to them, a Klingon commander named Kruge has intercepted information about Genesis and becomes interested in it (for much the same reasons as Khan: as a weapon). He travels to the Genesis Planet to learn its secrets after stealing additional information related to it. 
Spock's father, Sarek, visits Earth and discovers, with Kirk's help, that McCoy possesses Spock's "katra" (soul). Both his katra and body are needed to properly lay him to rest on his homeworld Vulcan; without swift intervention, Spock's consciousness will overwhelm McCoy, and he will also die. Disobeying direct orders prohibiting anyone from visiting the Genesis Planet, Kirk reunites with his bridge officers and goes through a series of highly unorthodox events such as Uhura charming the watch officer (locking him a closet), Kirk and Sulu springing McCoy from the Starfleet jail, Scotty hacking into the Starbase security system to open the massive base doors so the Enterprise can escape, and secondly disabling the pursuing USS Excelsior's "transwarp drive", by removing several circuits. 
Kruge arrives at Genesis first, accidentally destroying the Grissom with all hands (save for the landing party). He then summarily executes his weapons officer responsible for the Grissom's destruction; Kruge wanted prisoners. His crew locates and captures the scientists on the planet: David, Saavik, and a now-teenaged Spock. Kirk and the skeleton crew of the Enterprise arrive, unaware that the Klingon ship and its crew are cloaked nearby. Unable to hail the Grissom, the Enterprise crew suspects the presence of a Bird of Prey and are able to strike first, hitting the Klingon ship as it de-cloaks. The Bird of Prey fires back, overloading the Enterprise's automation systems. This disables all functions throughout the ship. Kruge demands that they surrender, and orders the troops that he had sent to the surface of the Genesis Planet to kill one of the prisoners as a show of strength. David defends Saavik, who was to be the intended victim, and dies as a result. Kirk is devastated to hear his son has been killed. 
Rather than surrender, Kirk orders McCoy and Sulu to the transporter room. Kirk, Scotty and Chekov order the ship to self-destruct, and they escape the Enterprise for the last time. The computer counting down confuses the majority of Kruge's crew who had just beamed over to complete the ship's capture; they are all killed as the ship self-destructs. The crew of the Enterprise watches from the planet's surface as their home for the last twenty years disintegrates as it enters the atmosphere. They find Saavik and Spock and free them from their captors. Moments later, Kruge beams to the planet and has everyone but Kirk and Spock beamed aboard his Bird of Prey. Still demanding the technology of the Genesis project, Kruge engages Kirk in hand-to-hand combat on the disintegrating planet. Kirk defeats Kruge, who plunges into a volcanic rift. Kirk quickly grabs Spock, and, imitating Kruge's voice, shouts the order to beam them both aboard Kruge's ship. The Enterprise crew are able to easily capture the Klingon vessel and the one crewman left on board. 
The crew travel to Vulcan, where Spock's katra is reunited with his body in a dangerous procedure called "fal-tor-pan"'. Dr. McCoy agrees to the ritual, knowing that it is quite risky for both him and Spock. The ritual is successful, and Spock is resurrected alive and well, though his memories are still extremely fragmented. The final scene, a brief discussion between Kirk and Spock, ends with Spock slowly remembering the man before him: "Jim. Your name is Jim."