When I arrived at the National Portrait Gallery, "Lucian Freud, Portraits" had only been open to the public for an hour, yet it was already teeming with Freud aficionados clinching their audio guides. Freud isn't Leonardo but the exhibition, which gathers more than a 130 pictures spanning 70 years, is bound to become a landmark, not least because the late painter was actively involved until it his death last July. It's almost Freud by Freud.

Curated by NPG's Sarah Howgate, the show sticks to a chronological progression, punctuated by clusters of paintings featuring the same sitters — including members of Freud's extensive family, his former assistant David Dawson, and performer Leigh Bowery. The resulting narrative is quietly academic, but it provides an in-depth insight into the development of Freud's technique: from the sleek, slightly surreal pictures of the 1940s — which prompted historian Herbert Read to call him the "Ingres of Existentialism" — to the furious impastos of his later years.

Running through the exhibition like a leitmotif is a striking series of self-portraits. As he took control of his medium, Freud was experimenting with the effects of his pictorial decisions directly on himself. Freud's self-portraiture — fulfilling the genre's traditional aim — was also a way for the artist to affirm his place in the world. The pale youngster in "Man with a Feather (Self-Portrait)" (1943) gradually morphed into the ghostly devil of "Self-Portrait Reflection" (2002), in which features are reduced to a fury of grey brushstrokes. Freud ceaselessly observed himself working, his eye growing sharper and crueller as he rushed toward the end.

A pivotal moment in the artist's career was his decision to stop sitting at the easel and to stand up and face the canvas, ready for a fight. "Hotel Room" (1954) was completed just before this turning point, and it exemplifies Freud's early period. The painter is pictured looking back at the viewer from a non-descript hotel room. In the foreground, his second wife, Caroline Blackwood, lies in bed, her blue eyes drowned in unshakable sadness. Soon the artist was to realize that the drama only really happens on faces and bodies, that anything else was anecdotal. With "Woman Smiling" (1958-9), the face of his former student and lover Suzy Boyt becomes a land to be conquered in all its changing hues and shifting textures.

The painter's world progressively reduced to his studio where sitters were called in to disclose their flesh on decrepit sofas. The claustrophobic repetition of this interior — wooden floorboards, yellowish walls, grey linen — exacerbates the bodies' idiosyncrasies: the taunt skins on the narrow hips of sleeping young girls and the rolls of fat in the portraits of benefits supervisor Sue Tilley. She had been introduced to Freud by Leigh Bowery, and was for a while Freud's favourite subject. He seems to have been fascinated by her sheer monumentality and painted her repeatedly, most famously in "Benefits Supervisor Sleeping" (1995), which sold for $33.6 million in 2008, the highest price ever paid for the work of a living artist.

"Lucian Freud, Portraits" ends with three nudes of Dawson and his dog Eli, including the artist's unfinished last painting "Portrait of the Hound" (2011). "I work from people that interest me and that I care about, in rooms that I live in and know," Freud once said. This last picture epitomizes the intimacy of the studio and the friendship uniting the two men. The dog is asleep and Dawson — who by then had been Freud's assistant for two decades — quietly returns the painter's inquisitive gaze, offering himself to his pulsating brushstrokes.