A tower structure including a central, vertical mast and a plurality of tensioned elongate elements arranged to support the mast against buckling, the plurality of tensioned elements together defining a generally hyperboloid structure and including a first plurality of elongate elements which define a multiplicity of junctions therebetween, a second plurality of junction-to-mast joining elongate elements which join at least some of the multiplicity of junctions to the central, vertical mast; and a third plurality of junction-to-junction joining elongate elements which are connected at a plurality of mutually spaced fixed locations therealong to the at least some of the multiplicity of junctions.