Some structures have physical shapes that allow them to operate over very wide bandwidths. Exponential slots and biconic antennas are examples. Others are a collection of narrow band antennas combined to provide wide coverage. A log-periodic dipole array is an example.
Vic Rumsey in the 60's started much work in this area by observing that antennas whose structures were defined by angles rather than lengths tended to be very broadband, think of spirals for example.
Kraus proposed a "volcano smoke" antenna for use as a broad band element.
Generally, "fat" antennas are broad band and "skinny antennas are frequency specific.