Over the years, both the Victoria & Albert in London and the Ashmolean Museum in Oxford had been extended behind their original buildings with rambling additions that resulted inchoate wholes. MUMA's work to form the V&A's new Medieval & Renaissance Galleries, and Rick Mather's rebuilding of a new Ashmolean behind Cockerell's original, embody two transformative approaches, in which recent museological notions of contextualised display have been invoked to enliven experience and knowledge. Each dramatically enhances its host's characteristics: one formed as a vast repository of national collections, the other from the personal collections and ambitions of a few individuals. The V&A project has radicalised part of the building's generic structure, whereas the Ashmolean reworks the museum form, constructing a different kind of container behind the nineteenth-century original. In both projects, the architecture and the curatorial intention coincide alchemically.

For a museum of such varied and significant collections, the Ashmolean's relatively small size makes its redevelopment seem ideal: a microcosm of the 'universal survey' museum. The institution's bold manoeuvre has been to represent the collections in a new museum form which feels more akin to the private collection from which the Ashmolean started, attached to Cockerell's neoclassical edifice built for Oxford University's art collection. Having demolished and rebuilt everything behind the original, a dual museum has resulted, which describes the typological shift in occidental museums of the past thirty years. While the original worked on a classic enfilade of galleries for the predominantly pictorial collection, Mather's new museum is of a modern spatial genre with a non-Iinear grouping of double and single height volumes interconnected in section to be intelligible as a whole, with two long axes hooking the new building into the old. The new galleries are rarely experienced as discrete entities. From most, three or four spaces are visible, with the building's main infrastructural system legible through its two full-height staircases attached to the main axes, and the syncopation of single and double-height galleries, with their controlled natural lighting. The visibility constraints set by Cockerell's building suggested a new volumetric strategy, squeezing five low storeys into the height. The Ashmolean's redisplay strategy, Crossing Cultures Crossing Time, is a means to link a series of varied, small but high quality collections with some, such as Islamic Middle East, placed in key connecting locations in the new museum. It neatly simplifies the open-ended complexity of a universal museum, capitalising on the Ashmolean's small size to represent the collections in a digestible whole and sustained by a spectacular white architecture.

The survey galleries, packed with rich collections such a European ceramics, still enable serious investigation and discovery. Reinforcing the new building's legibility and long views, the displays use freestanding cabinets, often visible from all sides and above, and cabinets set into thick service walls, many two-sided to maintain transparency. The low galleries (2.4 metres) resemble large displays, with their vitrines almost scraping the ceilings. The effect is to disrupt conventional containment with cross-sectional views and corner room openings, while simultaneously resembling an enormous cabinet of curiosities which recalls the Ashmolean's origins in the Tradescants' collection. 

Although this is being presented as a new museological approach, the scale of the museum, with its new spatial structure, has a looseness and fluidity that encourages the visitor to make connections which are as likely to be accidental as predetermined. The building simultaneously achieves a grand scale of the full-height volumes with their clear-cut unfiltering rooflights and the personal intimacy of the cabinet-like galleries.

The V&A's formation marked the categorisation of non-scientific artefacts encompassing occidental and oriental objects, and typological arrangements including its extensive china, glass and textile collections. The new presentation has assembled a spectacular range of its Medieval and Renaissance objects from different collections into ten themed galleries. The exhibition design has expanded to a substantial architectural project to reconfigure the south-east end of the Aston Webb building and alter its infrastructure by incorporating a lightwell into the building as a new gallery form. A coherent exhibition is formed from a wing of the building whose fracturing from the museum's body, through split levels, had been compounded by circulation which obstructed connections. The architecture has both developed a new design approach to the formation of display within the building's storehouse' halls, and unravelled the perverse complexity of the original configuration, with a potentially rippling effect on the museum's overall accessibility and structure.

The main architectural component of this reworking is an extraordinary three-storey-high glass-roofed gallery formed from an old lightwell void wrapped around an apsidal religious Gallery housing the Italian Renaissance anta Chiara chapel. This interstitial gallery is transformative to the Medieval & Renaissance display, and the museum's use in both dimensions, cutting through hall and floors in a modernist spatial contrivance to reveal lower and upper galleries beyond this collection. It contains a new strategically reconfigured stair and a glass lift, connecting this corner into the building's main east-west access, and north to the ironwork and oriental galleries and cast court - the museum split level apparent in the view squeezed under the thin concrete landing of the new staircase. This enables the incorporation into the Medieval & Renaissance suite of the original basement galleries that had never been used for purpose because they were inaccessible. The stair's placement also makes six museum levels accessible for the first time, with direct links, for example, to the Glass and new Ceramics galleries. 

The power of MUMAs architectural intervention is that it works on three levels: it shapes the Medieval & Renaissance display into an exhibition specific to the galleries in which it housed; the artefacts, thematically arranged, are attached to their social and physical contexts for the first time. Simultaneously acquiring individual status, they emerge from the old typological classification systems. This is a radical curatorial move, given the challenge of accommodating many objects of a vast scale range in large volume with little wall space. The design meticulously matches work to remade environments in an artless fusion of object and locations. Architectural and display techniques change the bland galleries into exhibitions, controlling light levels by altering ceiling profiles, with rich wall colours used for the intimacy of domestic space and its objects: ochred gold, dark green. A barrage of devices is used to create walls and form spaces: architectural objects such a Romanesque stone windows as dividers, onyx screens fixed over window as backdrops for crucifixes. A variety of objects, in often intense arrays, structure the spaces with display cases reduced to stone plinths and all-glass boxes, the antithesis of the endless rows of framed vitrines in the original galleries. The glass case over the huge angled religious processional rises to the full height of the gallery.

The architecture of the display establishes a hierarchy between the building and its exhibiting function - no longer does the grandeur of the building overpower its contents. Their context becomes that of the museum. The architecture also addresses the relationship between the exhibition galleries, giving a coherent narrative beyond the museum. The new interstitial space reinforces a strategy of breaking through me long sides of galleries to connect them, if not physically then visually, something the building's existing enfiladed gallery structure rarely does. The Renaissance domestic theme of Splendour and Society connects to Cityscape through a balcony formed from one of the architectural exhibits built into the gallery wall below, appropriately daylit to suggest an Italian piazza as a public drawing room. A timber window set into a lower gallery wall straddles the line of exhibit and architectural display, culminating in the new gallery where a sixteenth century spiral staircase and an early domestic timber facade, which had sat uncomfortably in the taxonomy of the museum, hang with the pathos of architectural fragments reflecting the overbuilt city.

The third level of context is to the museum. The infrastructural links made by tile new space imply the display's wider context. Long views through and across the galleries, resulting from the repositioned stair, link objects to the displays elsewhere in the building. In the Ashmolean, where the collections are smaller and more fragmentary, the display demanded a stylised theme to lend it coherence, which the building's spatial form, graspable in single views, achieves. At the V&A, where scale and complexity make it difficult to take in the galleries as a whole, objects are linked by implication.

The Ashmolean and the V&A are both interiorised architectural projects with refined engineering (in both instances by Dewhurst Macfarlane). In the Ashmolean, volumetric containment is apparently inexpressive but mannered in the detail of applied elements: the staircase handrails, the curves in landings and inflections to the steel bridges - technical motifs of a certain kind of contemporary architecture.

The V&A has an inexpressive strategy towards its technical interventions, at the scale of the architecture and the restrained means of support to the exhibits. Its strategy and crafting are the inheritors of the celebrated interventions by Carlo Scarpa at the Castelvecchio, but without their intensely mannered detailing. Both the Ashmolean and the V&A are culturally sophisticated, presenting their respective architects and engineers as informed collaborators with an understanding of how existing public institutions could work.

Ros Diamond is principal in Diamond Architects, based in London and Oxford.