Blender and texture issue

I’ve successfully created an object in blender and got it to appear in Unity: only a simple object, no animation or anything complex. What I wanted to do then was to apply a texture to it in Unity, just as I would to a standard cube or whatever. This kind of works, in that the object changes colour to (roughly) the colour of the texture (so eg a red marbled texture turns the object red), but the texture itself doesn’t appear.

Any help as to why this happens and how I get round it would be more than welcome.

(unity 3.3.0f4, blender 2.57.1)

You have to UV map your object.