The pair wrote books that detailed alleged monetary mismanagement in the Holy See.
Gianluigi Nuzzi and Emiliano Fittipaldi face up to eight years in prison if convicted of publishing confidential Vatican information.
However a number of organisations are supporting the journalists and are calling on the Vatican to drop the charges against the pair.
The Committee to Protect Journalists, Reporters Without Borders and the Organisation for Security and Cooperation in Europe all want the accusations dropped.
There has also been some controversy over the trial itself. It is claimed that hours before the trial neither they nor their lawyers had seen the court file detailing the accusations against them.
The pair were indicted on Friday but Mr Nuzzi only spoke with his Vatican court-appointed lawyer for the first time on Monday morning.
They risk arrest by walking on Vatican soil, however both arrived shortly before the trial was set to begin, saying they want to understand the accusations and to report to the world what transpires.
Mr Nuzzi said they would not be intimidated: "There is evidently an interest in distracting from the embarrassing disclosures."
Mr Fittipaldi added that they did not yet understand what they were being accused of doing: "The only thing we did was publish the news, which was not denied, and documents that tell of scandals."
Neither expected the Vatican would detain them and both journalists said they believed no Italian judge would extradite them, given that freedom of the press is guaranteed by the Italian constitution.
Mr Fittipaldi's book Avarice, and Mr Nuzzi's book Merchants In The Temple, both published earlier this month, make claims of waste and mismanagement in the Vatican administration, as well as accusing some cardinals and bishops as being greedy.
The books also chronicled the alleged resistance that Pope Francis is facing in trying to clean it up.
The three other people on trial are Monsignor Angelo Lucio Vallejo Balda, his assistant Nicola Maio, and Francesca Chaouqui, a commission member and public relations expert.
All three are accused of forming a criminal organisation and of procuring and leaking confidential documents.
Mr Nuzzi and Mr Fittipaldi are accused of publishing those documents and of "soliciting and exercising pressure, above all on Vallejo Balda, to obtain the documents and other reserved news", according to prosecutors.
The journalists deny the pressure accusation but acknowledge that they, like all journalists, obtained information and published it.
Ms Chaouqui has denied wrongdoing and was allowed to avoid detention after she co-operated with investigators. Mr Balda, who is in Vatican detention, and Mr Maio have not responded publicly to the accusations.
