Dave Chappelle’s best joke is himself. In this he isn’t unique: by a process of slow, bit-by-bit construction, the most successful comedians end up with a persona that transcends any punch line. The crowd begins to titter before a word passes through the P.A. system; familiar mannerisms overshadow syntax, however carefully arranged. Some comics come to resent this effect; others accept it as a crutch and their craftsmanship declines. A much smaller number sharpen the history they share with the audience and use it as a new tool, and sometimes as a weapon. (This might be one definition of greatness in standup.) The fable-like arc of Chappelle’s fame has placed him, over time, in each of these positions. Just before his dramatic escape from “Chappelle’s Show,” in 2005, he complained about people approaching his family at Disney World and yelling out catchphrases. In the years since, his digressive, minimally marketed sets at clubs across the country have often been derailed by hecklers—and, occasionally, by Chappelle himself. Two new, simultaneously released Netflix specials, “The Age of Spin” and “Deep in the Heart of Texas,” are evidence that Chappelle’s ongoing drama with his fans has borne artistic fruit: he has emerged, perhaps inevitably, as the most self-referential comic in recent memory—maybe ever.

Both specials begin with stories about his own performances. (He shows up catastrophically high to one, and has a banana thrown at him during another.) In “The Age of Spin,” he recounts a traffic stop that worried him, but not too much: “I’m black, but I’m also Dave Chappelle,” he says. In another bit about a ruefully funny confrontation, he and his sister walk down the street, she in Muslim garb, he “dressed as Dave Chappelle.” Chappelle organizes “The Age of Spin” around the four times he has encountered O. J. Simpson in person—he, too, was a fan of “The People v. O. J. Simpson”—but the anecdotes are less about Simpson than about the various stages of Chappelle’s career. One meeting happens while he lunches with his agents, celebrating a deal that later went sour; the last is at the Kentucky Derby, just after the end of “Chappelle’s Show,” and features a cameo by another “missing” comedian, Chris Tucker. When, more recently, he was dragged by his kid to a Kevin Hart show, Chappelle says, he got jealous. “I do this, too,” he tells his child, plaintive and annoyed.

This development in Chappelle’s work shouldn’t be confused with the confessional turn taken by many recent comics, from the gentle and self-deprecating Mike Birbiglia to the more jagged and provocative Tig Notaro, whose set “Live,” from 2012, focusses on a cancer diagnosis she had just recently received. For Chappelle, “Dave Chappelle” is more concept than individual; the name itself often qualifies as a laugh line, and Chappelle seems scornful of his fans for ever believing in the existence of his flatter alter ego. Chappelle deserves his reputation as a canny social satirist, but he has always been sillier than advertised: in both specials, but especially in the looser “Deep in the Heart of Texas”—during which, at one point, he takes a seat on his stool and crowdsources a cigarette—his closest resemblance is to an after-hours Bugs Bunny, spliff in one hand and black-studies syllabus in the other. One of the best moments in “Texas” is an absurdist catalogue of forensic discoveries by the rapper Lil Wayne. Chappelle remains one of the best storytellers alive, booby-trapping his narratives with head fakes and hilariously astute turns of phrase. But even the most personal story here, about an extortion attempt that he reports to the F.B.I., and the marital trouble that follows, is told as a series of cartoonish indignities. You never mistake his disclosures for signs of intimacy—he’s always steering toward his persona and away from his person.

Meanwhile, Louis C.K., whose new special, “Louis C.K. 2017,” was released last week—also by Netflix, which may have wrested the “home for comedy” mantle away from HBO for good—has made a different use of himself. Where the crucial element in Chappelle’s mystique is scarcity, C.K. has, in the past decade or so, been almost compulsively prolific. His efforts have spanned several genres and degrees of seriousness—besides his annual standup specials, he has created three television shows: “Lucky Louie,” a short-lived faux-sitcom; the much heralded surrealist comedy “Louie”; and, most recently, “Horace and Pete,” a dark, desperate teleplay descended from “The Iceman Cometh.” This variety has had a depressurizing effect. Each work contains a shard of C.K.’s personality, and none carries the burden of representing the whole. The result is a kind of self-effacing freedom.

In “Louis C.K. 2017,” he acknowledges the fundamental absurdity of the standup’s recent designation as a purveyor of sociopolitical opinion. “Here’s what I think,” he says, almost rolling his eyes at himself, as he eases into a finely parsed opening routine on abortion. He rejects applause when he lavishes praise on public-school teachers: “I don’t recommend clapping at anything,” he says. “You’ll regret it at the end of the thing.” He disdains, but can’t help participating in, the stupidest, most solipsistic modern conventions, such as “reading your own already-sent e-mails.” He is perched, he says, on the “razor-thin margin” between liking life—not loving it—and committing suicide.

C.K. is silly, too. He knows that stereotypes are bad, but can’t shake his feeling that caricatured accents are funny. (He uses them at home, in front of his kids.) One particularly trippy bit spins outward from his daughter’s semantic confusion over the phrase “9/11 deniers.” He has developed, over time, a Pagliaccian facial precision: one of the funniest moments in “2017” is silent: a droopy, sad-sack impression of a thwarted ISIS combatant. (Chappelle aims for the air in the group’s tires, too: “ISIS is at the top of the terrorist charts!” he says.) Later, he looks up at an imagined boyfriend with an adorable pout.

What happens when these differing selves—Chappelle the fame-flattened trickster, Louie the philosophical clown—consider a changing world? Each has passed through his peak as the “heavyweight champion of standup,” and both bear the physical marks of time’s passage. (Chappelle has put on what looks like forty pounds of muscle; C.K., famously schlubby, has dropped his old uniform of jeans and a T-shirt for a suit and tie.) Both are preoccupied by the present. “Louis C.K. 2017”—he has insisted that his name is part of the title—sounds like the label scrawled onto the back of a photograph. What does it mean, he seems to ask, to be me, right now? “Your circle of concern tightens,” he says, explaining why he has trouble mustering sympathy for pets. “I have four nephews, and I don’t love any of them,” he adds, after a beat. But, perhaps because he mistrusts himself above all others, he seems unthreatened by the times. When he talks about becoming more aware of transgender individuals, he turns self-reflective, and then slightly envious—he wishes that he could figure out, once and for all, his own identity, as he imagines these folks have figured out theirs.

For his part, Chappelle seems befuddled. “The Age of Spin” refers to a line in the special in which he laments the atomized confusion and fatigue caused by the news. For him, this is “the age where nobody knows what the fuck they’re looking at.” It’s a good point as far as it goes. It betrays, too, a nostalgic streak that has gradually become Chappelle’s stock-in-trade. He kids his younger audience members: “You gotta Google shit that I went through,” he says. Amid this “shit” is a memory of being in the classroom and watching live on television as the Challenger_ _exploded. This immediately recalled, for me, a point made by the narrator of Ben Lerner’s novel “10:04.” “I don’t have a single friend who doesn’t remember watching it as it happened,” the narrator says of that disaster. “The thing is,” he continues, “almost nobody saw it live.” Hindsight isn’t always so clear.