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Inserting an image into any object is easy - cropping it isn't.

To insert an image, select the shape, then open the Style:Image inspector and either drag and drop the image to the image well, or select the Image check box and choose the image you want inserted:

Then pick the style of the inserted image (stretched etc). You can approximate cropping by picking Natural Size and fiddling with the Scale etc and dragging the image to fit the shape, but it is easier to crop it in an image editor first and drag and drop the cropped image.

Note, to quickly add an image to an OmniGraffle document, simply drag and drop it onto the canvas.