A businessman has taken Google to the High Court in London in what is being seen as a landmark case over "the right to be forgotten".
He is challenging Google's decision not to remove a criminal conviction he has from the 1990s from search results.
People can ask for online information to be removed from searches if they feel it is outdated or irrelevant.
Google said it would "defend the public's right to access lawful information".
"We work hard to comply with the right to be forgotten, but we take great care not to remove search results that are clearly in the public interest and will defend the public's right to access lawful information," the firm said in a statement.
The search giant has been asked to delist nearly two million search results in Europe, and has removed more than 800,000 of them.
The right to be forgotten is a legal precedent set by the Court of Justice of the European Union in 2014, following a case brought by Spaniard Mario Costeja Gonzalez, asking Google to remove information about his financial history.
The UK case revolves around a businessman who wants Google to delete links to a criminal conviction for false accounting in the late 1990s. His conviction is deemed spent under the Rehabilitation of Offenders Act 1974.
The man cannot be named due to reporting restrictions surrounding the case.
The man is being represented by law firm Carter-Ruck, which has yet to respond to requests for comment.
The General Data Protection Regulation, a sweeping change of EU data rules, is due to come into force in May and aims to extend the law to make it easier for citizens to have content removed.
The current case is being heard by Mr Justice Warby and is expected to last several days.
A similar case is due to be heard next month.