The landmark case, which was launched in 2008, was brought by four Nigerian farmers who insist that spills from the oil firm's pipelines damaged their crops and fish-farms and destroyed their livelihoods.
It marks the first time a Dutch company has been sued for alleged environmental mismanagement abroad.
Lawyers of the villagers from Goi, Oruma and Ikot Ada Udo, urged The Hague Civil Court to rule Shell liable for poisoning their farmland.
One of the plaintiffs, Friday Alfred Akpan from the village of Ikot Ada Udo, told the BBC : "Fish died as a result of the oil spill, making it difficult for me to live and put my children through school."
His fellow plaintiff, Eric Dooh, told reporters outside court: "If you are drinking water you are drinking crude, if you are eating fish, you are eating crude, if you are breathing, you are breathing crude."
He added: "What I expect today is justice... I expect that judges are going to proceed in this matter, have sympathy and look into our environment - tell Shell to apply international standards where they are operating in Nigeria."
The villagers blame the leaks on corrosion of the pressurised underground pipes.
The Anglo-Dutch firm, however, has denied responsibility, insisting that more than half the leaks are caused by theft and sabotage.
A Shell official, Allard Castelein, told the BBC: "I mean, there's video evidence. There's signed testimonies by joint investigation teams that are constituted of the local municipality, the company, the government."
An earlier Dutch court ruling accepted Shell's assertion that the leaks were caused by sabotage but the farmers are currently fighting to have it overturned.
If the villagers are successful in their suit, campaigners said that it could set a legal president, opening doors to further compensation claims against international companies.
A judgment in the case is expected early in 2013.
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