The actor and director are now 67 and 68 respectively, but neither seem to be contemplating retirement, and at last year's Berlin Film Festival they hinted that they might make a sequel to perhaps their most critically acclaimed movie, Taxi Driver. That would be something to savour, but meanwhile there's The Irishman to look forward to.
Since they first worked together in 1973, the pair have created some of the most iconic moments in American cinema, and their careers are inextricably linked in the way that John Ford and John Wayne's were.
Though both were born in New York and raised in and around Little Italy, Scorsese and De Niro's paths did not cross when they were growing up, and both had embarked on their respective careers by the time they met. After making an acclaimed string of short films in the mid-1960s, Scorsese entered the circle of the so-called 'movie brats', Francis Ford Coppola, George Lucas, Steven Spielberg and Brian De Palma. And it was De Palma who introduced him to De Niro.
De Niro had worked with Brian De Palma on Greetings and The Wedding Party, and De Palma was hugely impressed by his dedication to his craft. De Niro had already embarked on his obsessional, Method-based approach to film-acting, and in Scorsese he found a kindred spirit.
Their first film together, Mean Streets (1973) is sometimes overlooked by mainstream audiences, but was hugely influential and a sign of things to come. De Niro co-starred with Harvey Keitel in this gritty crime drama about two minor hoodlums on the fringes of the New York mafia, and De Niro's portrayal of the violent and volatile Johnny Boy was a revelation.
Scorsese mixed the themes of guilt and Catholicism with a period pop soundtrack so successfully that he even managed to impress the New Yorker's legendary and fearsome critic Pauline Kael, who called it "a true original, and a triumph of personal filmmaking". What came next, though, would put Mean Streets in the shade.
De Palma again had a part to play in the genesis of Taxi Driver (1976). According to Scorsese, it was De Palma who introduced him to Paul Schrader, a talented young screenwriter who'd just written the script for the Robert Mitchum movie, The Yakuza. Schrader had an idea for a story about a New York cabbie who loses his marbles and turns vigilante, and Martin Scorsese latched on to it immediately.
Scorsese conceived a dream-like backdrop to Travis Bickle's increasingly confused world. He used saturated colours and a woozy soundtrack from Bernard Herrmann to augment his sweeping shots of ramshackle 1970s New York. And he coaxed an exceptional, star-making performance from Robert De Niro.
A photo exists of Scorsese crouched just out of shot in the film's famous mirror sequence, where Travis Bickle taunts his reflection before pulling out a concealed gun. Scorsese was in De Niro's ear the whole time, hidden in the back of Bickle's cab during those moody rides around Manhattan.
The director's personal life was in disarray at the time, and he was struggling with a drug habit, but this only seemed to add to Taxi Driver's paranoid power.
Martin Scorsese's cocaine use spiralled during the making of New York, New York, an ill-conceived musical tribute to his hometown starring De Niro and Liza Minnelli, with whom the director had become romantically involved. Though not without its moments, the film didn't break even and was considered a step backwards after the triumph of Taxi Driver.
It was Robert De Niro who rescued Scorsese from a dangerous slump by persuading him to make a film about 1940s middleweight boxer Jake La Motta. La Motta was a kid from the Bronx who fought a series of epic battles with Sugar Ray Robinson before succumbing to a self-destructive spiral. It was this that Martin Scorsese would empathise with as he created his masterpiece, Raging Bull (1980).
The scenes in which he pictured De Niro sparring in black and white are justly celebrated, as is De Niro's performance. There was much hype at the time about the 50 pounds he put on to play an older La Motta, but this was mere detail compared to the performance itself, which was so intense it reminded critics of the young Marlon Brando.
Scorsese and De Niro took a bold step with their next project, a darkly comic story about a failed comedian who kidnaps a talk show host in order to get on prime time television. King of Comedy (1983) is now very highly regarded, but did badly at the box office at the time.
They took a break from each other through the late 1980s, as De Niro expanded his range and Scorsese courted controversy with The Last Temptation of Christ. But they teamed up again in 1990 to make one of the most iconic gangster pictures of them all.
In GoodFellas, De Niro, Ray Liotta and Joe Pesci played three amiable hoodlums on the fringes of the Brooklyn mob who cheerfully extort, steal and kill through the 1950s and '60s.
Like practically all Scorsese films, it was a morality tale. The director had been fascinated by mobsters since seeing them swagger around Little Italy in his childhood, and in GoodFellas he married music, story and style quite seamlessly to create a moving, shocking and surprisingly funny film.
Scorsese and De Niro's 1991 remake of the J Lee Thompson classic Cape Fear was altogether less convincing, with De Niro's portrayal of remorseless psychopath Max Cady frequently approaching parody.
They were on altogether firmer ground with the 1995 Las Vegas-based gangster film, Casino, a dark and very violent tale of gambling empires and deadly rivalry that co-starred Sharon Stone and Joe Pesci.
Since then, and despite many near misses, Robert De Niro has not appeared in a Martin Scorsese film. He was due to play Frank Costello in The Departed but had to pull out, leaving the role to a no-doubt grateful Jack Nicholson. But the plans for The Irishman seem firmly fixed, which is exciting news for film lovers everywhere.