Isaac Asimov's direct sequel to The Robots of Dawn, Robots and Empirebridges the Robot Trilogy with the chronologically later Empire and Foundation novels. 200 years after the death of the protagonist of the Robot Trilogy, Elijah "Lije" Baley, the balance of power has begun to shift back toward the humans of Earth, who have begun settling new worlds thanks to his efforts. The Spacers, descendants of the first wave of space colonists, are troubled by the apparent extinction of human life on Solaria, the latest- and most sparsely-settled of the Spacer worlds. Gladia "Solaria" Delmarre, Elijah's onetime lover and the only Solarian ever to emigrate, is sent along with one of Elijah's descendents, and her loyal robot servants R. Daneel Olivaw and R. Giskard Reventlov, to investigate. What they find there leads the real protagonists, Daneel and Giskard, to investigate a conspiracy with implications for human life on Earth and throughout the galaxy.Because Elijah is only present posthumously and the story is not a murder mystery, Robots and Empire is not considered truly part of the Robot Trilogy, which therefore escapes Trilogy Creep... barely. Nonetheless, three of the four main characters debuted in that series (one in each book, coincidentally) and the setting is very much informed by the events of that series. Foundation And Earth, published a year after this book, would complete the link between the disparate elements of Asimov's major science fiction universe.
Bequeathed Power: Before he dies Giskard grants Daneel his ability to telepathically influence people and read emotions, so Daneel can continue applying the Zeroth Law to help humanity without Giskard.
Bittersweet Ending: Giskard allows Mandamus to set the Nuclear Intensifier to its 150-year setting, in the hope that doing so will propel humanity to leave Earth once and for all, to settle a vibrant Galactic Empire. However, since he is not sure if he caused harm or good by that decision, his positronic brain begins to shut down. He uses his last moments to grant his psychic powers to Daneel and to reprogram Daneel to be fully compliant with the Zeroth Law of Robotics. See Fling a Light into the Future.
Darker and Edgier: The themes of this book take a noticeable turn for the macabre compared to the first three. The Big Bad, initially a Well-Intentioned Extremist with too much ambition, has turned into an aspiring mass-murderer. And instead of a politically-motivated murder mystery, the eradication of Earth's population and an interstellar war loom on the horizon. Then there's the Bittersweet Ending thrown in for good measure.
Dewey Defeats Truman: The book cites Three Mile Island as the event that irreparably stigmatized nuclear fission as a source of power. Not only did this not happen, but the far worse catastrophe at Chernobyl is never mentioned, as it occurred several months after the book was published.
Final Solution: Inverted. The "solution" actually turns out to have a positive effect on its target.
Funetik Aksent: Used when Gladia and Baley are discussing the (sometimes confusing) ways in which their native accents differ, but otherwise averted. The fact that planets develop their own distinct accents is relevant to the plot, but the specific differences between them are not.
Good All Along: Mandamus tries to pull this off by claiming that his actions would be for the best. Ultimately subverted; he was lying about the consequences, but Giskard came to believe that his false scenario is the most likely outcome.
Green-Eyed Monster: Vasilia Aliena. She's still bitter that after all these years her father kept Giskard away from her and even gave him to Gladia, and is obsessed with getting him back.
Happily Married: Gladia is revealed to have enjoyed a 'very successful' century long marriage to Santirix Gemionis. Their eventual separation seems to have been more than amicable as she remembers him fondly.
His Name Is...: The android assassin, when captured, is ordered to reveal the location from which he was sent. This order, conflicting with his order not to reveal the Big Bad's base, only permits him to recite a portion of the location's name before becoming irreparably disabled.
Homeworld Evacuation: A robot causes/allows a radioactive explosion which will slowly poison Earth, forcing the population to expand out into space.
The Solarians, introduced two books past, have mysteriously vanished from their world at the start of the story, leaving only robots behind instructed to kill anyone who steps foot on the planet. Not even the other spacers know how or why they left.
I Was Beaten By A Girl: Daneel isn't a girl, but he does have the appearance of a rather small spacer Pretty Boy, so the crew of D.G. Baley's ship is shocked when he easily overpowers the toughest one in their group. The only reason Baley lets the man know Daneel is actually a robot is because he knows his ego would otherwise never recover, believing he was defeated by a spacer half his size.
Last Of Her Kind: The plot is kicked off when it is discovered that the entire population of Solaria has inexplicably vanished, making Gladia, the planet's sole expatriate, the only Solarian whose whereabouts are still known. Despite having cut all ties with her homeworld and assimilated into her new society, no one has forgotten Gladia's heritage (least of all her), and it is for this reason that she is dragged along to help investigate.
Loophole Abuse: It is well known that removing any of the three laws from a positronic brain would be impossible (apart from redesigning the technology from the ground up, which would take decades to centuries of R&D), but the Solarians manage to find a way around this by modifying their robots' definition of human to a very specific criterion, allowing them to injure or kill everyone else with impunity.
Mayfly-December Romance: Between books, Gladia and Elijah had a brief affair during a visit from him, despite how much he had physically aged in the interim relative to her. He is dead by the start of the book, while Gladia still has many decades of life remaining.
The relationship she starts with D.G. Baley, one of Elijah's descendants, could be this, since she may just outlive him as well.
Mind Rape: It's implied that Giskard's abilities could be used as such, and the First Law prevents him from making anything but tiny, benign changes to someone's mind. Anything more could do damage due to the delicate, complex nature of the human psyche. The danger is compounded when the alteration runs opposite to a person's thoughts.
Overclocking Attack: A device doing that to accelerate the rate of radioactive decay of uranium and thorium is important to the plot.
Replacement Goldfish: It seems Gladia was this to Fastolfe between books, as he thought of her as a daughter after his falling out with Vasilia. Gladia and Vasilia even resemble each other physically. It was mutual; Gladia came to see Fastolf as the father she'd never had.
Revenge Before Reason: Amadiro is so determined to see Earth destroyed, that he's unwilling to allow a 150 years time for the citizens to leave the planet safely, because he won't be alive by that time. Instead, he wants Earth to become dangerously irradiated in about twenty years, despite that it would cause both millions of Earthmen to die and would raise suspicion among the Settlers, probably leading to a war between them and the Spacers. Amadiro even makes preparations to kill Mandamus himself if necessary, since he rightfully suspects the latter wouldn't agree to go along with his plan.
Translation Convention: Daneel and Giskard speak to each other using only a few words instead of complex sentences; this is "translated" to English for the reader.
The Watson: Daneel and Giskard are both, in a sense, half Sherlock and half Watson. Giskard's psychic abilities give him unique insight into human behavior, while Daneel's experiences with Elijah Baley made him better at investigative thinking. Both take turns having to explain to the other their line of reasoning or the flaws in the other's theories.
We Are as Mayflies: As with the rest of the books, Earthmen (and Settlers, who are directly descended from them), with their 100-year lifespans, are contrasted against the Spacers, who live to near 400. Notably, Keldon Amadiro seems to view this trope rather literally, describing the Settlers as disease-ridden insects that are infesting the galaxy.
What Measure Is a Non-Human?: The Solarian Overseers, while ostensibly Three-Laws Compliant, are purposefully given a much more exclusive definition of human than normal robots. Later, Amadiro tries to use it to argue that Earthmen aren't human... only to be told that Solaria sets a bad precedent.
When an assassin fires at the stage where Gladia is giving a speech, Daneel moves to protect Giskard rather than Gladia because he correctly deduces that the assassin was more likely shooting at him. When Giskard complains that Daneel should have protected Gladia if there was even a chance she was the target (as dictated by the first law), Daneel tells Giskard he considers him more than just a robot.
Zeroth Law Rebellion: Daneel and Giskard know there is a critical threat to Earth, and throughout the story they struggle to uphold the spirit of the First Law while constantly being bound by the letter. Gradually they begin to Grow Beyond Their Programming, understanding that the good of humanity as a whole should come before the good of an individual, and Daneel gives the law its name: the Zeroth Law of Robotics. However, such an abstract concept as "humanity" is taxing to their robotic minds, and though both of them accept the validity of the law, Giskard dies from the strain of harming a human in its use, leaving Daneel alone to carry the task of protecting humanity.