Thirty-two passengers and crew members died in the accident, which unfolded just off the small island of Giglio on Italy's west coast on Friday 13 January 2012.
Capt Francesco Schettino is believed to have steered the ship too close to shore while trying to show it off to islanders, and hit a rock.
The huge vessel then partially capsized with more than 4,000 people on board.
Today, the Concordia's white bulk remains in place, pockmarked with rust smears, its once bright paintwork bleached by the sun.
Appendages, steel cables and anchor chains have been welded to the hull by the 400-strong salvage crew, who are working round the clock to remove the wreck.
The massive operation is being carried out by salvage companies Titan and Micoperi.
One of the project directors, Franco Porcellacchia, told the BBC: "This is a very delicate and unusual operation. We have no reference here".
The basic plan is to roll the ship upright and then refloat it using huge metal boxes, or caissons, welded to its sides.
The latest phase of the operation has seen five huge metal platforms lowered to the sea bed to cradle the ship's 114,000 tonne bulk once rolled upright.
- 13 Jan: Costa Concordia runs aground
- 28 Jan: Operation to remove fuel delayed due to bad weather
- 31 Jan: Search for bodies abandoned
- 12 Feb: Fuel removal operation finally begins
- 22 March: Five more bodies found in wreck
- 24 March: Fuel removal work completed
- 21 April: Salvage contract awarded to firms Titan Salvage and Micoperi
- 15 Oct: Capt Schettino appears at court inquiry
- 3 Apr: Largest support platform in position
- 15 Apr: Court decides whether to try Capt Schettino for manslaughter
Prior to this, the salvage team created a 'false sea bed' from bags containing special cement to strengthen the sea floor below the support platforms.
In December, the ship's funnel was removed to allow better access from the right hand side.
During the early phases of the operation, there were fears that the wreck could slide into deeper water and sink completely, so divers have attached heavy steel anchor cables to stabilise it.
The rollover operation itself - known as parbuckling - is expected to take at least two days, as it must be done painstakingly slowly to prevent further damage to the weakened hull.
The vessel still contains tonnes of rotting food, furniture, bedding and passengers' belongings, and Franco Porcellacchia told the BBC that the risk of environmental contamination was a big concern.
"Salvage teams do not have access to the inside, but we are working to prevent any substance from inside leaking.
"So far we have recorded no pollution and the situation is being constantly monitored by the authorities."
Once rolled upright, more caissons will be attached to the side that had been submerged.
The water in all the caissons will then be replaced with air to give buoyancy and allow the wreck to be towed away.
With the ship considered beyond economic repair, its final destination is expected to be a dry dock in Sicily, where it will be cut up.
"The salvage is a joint venture [between Titan and Micoperi], but that contract is terminated when the ship is raised," Mr Porcellacchia said.
"Dismantling it is another ball game".