French-born New Yorker Louise Bourgeois (1911-2010) is perhaps the greatest female artist of the 20th century. She is also one of the greatest artists full-stop, but her work is powerful because it expresses the hunger and ferociousness of a particularly female kind of experience.

This exhibition has all the familiar Bourgeois elements: a huge sculpture of a spider, symbolic of the mother, spirals that point to the eternal return of her childhood trauma, and "Cell (Eyes and Mirrors)" (1989-93), a large installation made of walls of wire and broken glass, which fence in an abstract sculpture suggestive of fly-like staring eyes. Mirrors are turned this way and that, not quite reflecting one another. To peer inside this mythical medieval torture chamber is to glimpse the psyche of a brilliant woman. Here the past is waging a relentless attack on the present, and there’s no escape.

Such is the power of Bourgeois' vision that she could endow objects with an energy so violent and yet so attenuated to the discipline of sculpture, painting, and story-telling – examples of which are all included here. However, this exhibition lacks something – the large rooms are sparsely curated, which serves to illuminate the particular qualities of each piece, but seems unsatisfying. There is not enough work to fill the space.

Many of the works point to Bourgeois' prodigious output. They are the furtive workings-out of an imagination constantly in motion. Some are not immediately recognisable as Bourgeois, such as the minimalist red spirals on handmade Japanese paper, which cover one wall. Others are touching: "10am Is When You Come To Me" (2006) is a series of watercolours, etchings, and gouaches which show disembodied red hands reaching into view, emblematic of her thirty year friendship with her assistant, Jerry Gorovoy.

There are surprising and subtle moments: one of my favourite works here is "Amoeba" (1963-65), a bronze sculpture painted white, which clings, frog-like, to the gallery wall. Indeed, a frog or some less natural life-form seems to be writhing beneath the covering that encases it and pins it down. There is the frustrated, explosive sense of something trying to get free of something else.

Across the city at The Fruitmarket Gallery, there is a more compelling exhibition of Bourgeois' works on paper, including "I Give Everything Away" (2010), which show how she transformed her terror into art with escalating power right until the end of her life.