Reviewed: Drawing, Thinking, RHA Gallagher Gallery, until November 7th

Paul Coldwell, Arthouse until November 9th, Graphic Studio Gallery until Saturday

Arnott's National Portrait Awards Exhibition, Arnott's Exhibition Hall until October 29th

The RHA Gallagher Gallery is a hybrid that encompasses on the one hand the rock-like conservatism of the academy and on the other the shifting sands of post-modernity. Drawing, Thinking, the current show curated by education officer William Gallagher and director Patrick Murphy, is a brilliant response to what might be seen as the gallery's mixed constituency.

The exhibition is, in essence, an exploration of the current state of drawing. Rather than merely going through a list of fashionable practitioners and inviting them to submit examples, the curators have really searched out works that demonstrate the scope of drawing activity within and beyond the frame of fine art.

The show doesn't have a thesis. It's open-ended, but it is extraordinarily affirmative. While, taking it as a whole, it's difficult not to conclude that drawing permeates the way we interpret our world, it could be that this is something that is true at our historical moment for the last time. Day by day, digital media are appropriating more and more areas that were previously the preserve of drawing of one sort or another, and apart from being referred to by implication, this is the one area not seriously addressed in the selection.

The inclusion of architects Robert Venturi and Louis Kahn is relevant here, as computer screens and outsize printers supplant drawing boards in architect's offices, and CAD becomes a basic standard of professional literacy.

Yet even here, the evidence is that drawing is such an instinctive, direct, ubiquitous activity that it will never be entirely dispensable, though it is being displaced. It's there even in Venturi and Kahn's extremely elliptical (and not wildly exciting) sketches, which in just a few lines convey their different, distinct sensibilities.

Romek Delimata's storyboard is another case in point. Accompanying a terrifying piece of animation called Gravity, it is beautifully done but is also a reminder that films are planned and drawn on storyboards, usually in exceptional detail, though computers are making inroads there as well. Which brings us to the piece de resistance, William Kentridge's film, Felix in Exile, from 1994. It's not as contradictory as it might seem to nominate a film as the centrepiece of a drawing exhibition. A brilliant, sophisticated piece of animation which looks rudimentary in technological terms, it is literally drawing in motion, a drawing that continually remakes itself before our eyes, and is visually and narratively ambitious. It's worth a visit in itself.

Thomas Ryan, an ex-RHA president, provides an example of the traditional idea of the artist's sketchbook, something close to a visual diary, stocked with passing observations and thumbnail sketches. The sketchbook is still indispensable for artists of every persuasion, though not necessarily in that form, and may not involve drawing at all. One suspects that it does in the case of Marlene Dumas, whose beautifully fluent work has an extraordinary immediacy. Her relentless, wordy self-analysis strikes a chord with Patrick Graham. He and Charles Cullen, who shows a terrific three-dimensional City drawing, hold up very well in any context. Have we appreciated them enough at home?

There are several examples of artists who, in various ways, use drawing as a means of making personal maps of their worlds, from the obsessive quality of Stephen Brandes's date-stamped line drawings to Susan Tiger's fanatically precise accounts of individual objects. Kathy Prendergast would have been a useful addition here, given her consistent, related interest in both drawing and maps.

Gary Coyle's charcoal renderings of scene-of-the-crime photos are among several allusions to drawing's problematic relationship to photography. Nick Miller's colour drawings take on da Vinci's famous squared-circle study of Vitruvian man. It seems fair and accurate to suggest that the blistering urgency of Miller's work relates to his desire to produce not representations at all, with the implication of being at one remove, but intimations of living, physical presence.

Liam Belton, who is attempting a conceptual development of mainstream technical virtuosity, finds an echo, strangely enough, at the opposite end of the room, in Alice Maher's fetishised renderings of hair. It is not a survey show, and doesn't pretend to be, so it's no surprise that many artists are omitted, but less forgivably there are also significant and extensive areas of drawing that are simply not covered, specifically whole swathes of illustration, apart from the brilliant example of Michael Craig.

Such fields as caricature or archaeological or botanical illustration are ignored. But it remains challenging, innovative and stimulating.

Paul Coldwell's By This I Mean is a useful pendant to Drawing Thinking, in that it's about an artist learning to incorporate digital media into his working method. Coldwell describes himself as "a sculptor who makes prints, makes drawings, works with a computer, whatever", which after digesting the various strands of a large, varied and extremely ambitious exhibition seems a fair enough description.

Still, it's the sculpture that is most impressive. Without it, everything else would seem slickly accomplished but little more. His sculptural work focuses on everyday objects, but never straightforwardly. Either they are mapped by three-dimensional bronze or wood grids, or they emerge, in pristine clarity, from what might be described as impossibly realistic pop-up books. Coldwell effectively approaches the human subject and human experience in terms of these notional, almost Platonic domestic objects. There are elaborate, perhaps over-elaborate rationales in each case, outlined in the show's catalogue, but what pleases is the metaphysical weight with which he manages to invest each humble object.

While the Arnott's National Portrait Awards Exhibition doesn't attain fantastic standards overall, it includes more than enough strong work to make its return very welcome. There is clearly a great deal of interest in portraiture, an interest that the annual awards show helps in no small way to foster.

It features an exceptional amount of capable, thoughtful representational painting. Artists like Joe Dunne, Sheila Pomeroy, John Short, Desmond Kenny, Paul Funge, Blaise Smith, Tom McGuirk, Paul MacCormaic, John Mulvany and Ciaran Murphy make up a strong core. Photography, strangely, hardly figures at all, but Rachel Ballagh makes a good case for it with her self-portrait.