What debris has been found and what does it mean?
The company posted a one-line note on its website saying it had stopped "all exploration and commercial operations".
On its website the company had also advertised tours of the Portuguese archipelago of Azores and the Bahamas.
An investigation is ongoing into how the sub imploded during a dive to the Titanic wreck on 18 June.
Led by the US Coast Guard, authorities said the inquiry would aim to prevent similar accidents in future.
Chief investigator Cpt Jason Neubauer said last month that the Coast Guard had convened its highest level of investigation, and that the probe would be run jointly with Canadian, UK and French authorities. The investigation would be able to recommend civil or criminal charges, Cpt Neubauer said.
On 28 June the Coast Guard said debris and human remains from the Titan had been recovered and returned to land - concluding an early stage of the investigation. Authorities said the debris would be taken to a US port for more analysis.
Cpt Neubauer said in a statement last week that there was still "a substantial amount of work" left for investigators.
OceanGate's CEO Stockton Rush, 61, died on board the Titan alongside the four other passengers: British-Pakistani businessman Shahzada Dawood, 48, and his son Suleman, 19, British businessman Hamish Harding, 58, and Paul-Henry Nargeolet, 77, a former French navy diver.
Rush earned a reputation as an ambitious explorer and a passionate leader, one who occasionally broke rules to pursue his dream of exploring the sea.
He was on board the Titan for several successful dives, though he had reportedly ignored warnings over the safety of his sub.
-- Courtesy of BBC News