He is the fourth eldest of the Endless, and is depicted as a big, red-haired, bearded man. He wears colourful clothes with no particular theme. When Delirium and Morpheus encounter him in the seventh collection of issues in the series, Brief Lives, he has taken to wearing his hair in a ponytail, and owns a talking dog, Barnabas. Since he abandoned his responsibilities there is no sigil in the galleries for him, though he keeps his own gallery (wherein is a sword, his sigil). His realm is not portrayed in the series.
Destruction abandoned his realm and his responsibilities some time around the turn of the seventeenth century. He did not cease to exist as the active aspect of Destruction, he simply stopped directing the affairs over which he has control. As he says, destruction did not stop, it was merely no longer ordered and controlled. Destruction features most prominently in Brief Lives, in which his siblings Morpheus and Delirium set out to track him down. When they finally meet they do not exactly argue but talk at cross-purposes; Destruction's choice of path baffles and to some degree infuriates Morpheus, while Destruction finds it hard to comprehend Morpheus' position and concentrates on trying to impart to him some wisdom on the necessity of change and self-knowledge. Delirium just wants her brother back; she is reliant on her siblings for support, particularly her elder brothers.
Destruction is self-obsessed in the most positive sense of that term; after giving up his responsibilities he concentrates instead on attempting to learn about his own nature and exert control over it. This is manifested in his deliberate attempt to subvert his own essential nature and create instead of destroying; he is shown at various points writing indifferent poetry, painting an indifferent picture, cooking a meal left untouched by those for whom it was intended, and brewing Greek coffee which Delirium fails to drink properly.