Alexander is the chairman and founder of the Viasna Human Rights Center and former vice president of the International Federation for Human Rights. He is a laureate of the Andrei Sakharov Freedom Prize and other international human rights awards. He was nominated for the Nobel Peace Prize five times and won it in 2022.
Alexander had previously been prosecuted. On August 4, 2011, he was arrested after Lithuania and Poland handed over his bank account information to Belarusian authorities. He was charged with concealing income on an especially large scale. On November 24, 2011, the court sentenced him to imprisonment in a maximum-security penal colony with confiscation of property. Alexander pleaded not guilty, claiming that the funds were used exclusively for human rights activities. EU countries, the United States, and international human rights organizations recognized him as a political prisoner, and his sentence was politically motivated. He was released in the summer of 2014 under an amnesty.
On July 14, 2021, Alexander was arrested again following a search of his apartment and office as part of a tax evasion case. In September 2022, that case was dropped, but he was charged with new charges of smuggling and financing group activities that grossly violate public order.
In March 2023, he was convicted and sentenced to imprisonment and ordered to pay substantial compensation. He pleaded not guilty in court.
In early November 2023, Alexander was placed in a PKT for trumped-up reasons. In April–May 2024, he was returned to his unit, but he continues to be under increased scrutiny. He works in woodworking, receives penalties, and is deprived of parcels, video calls, and correspondence. It is known that his previous stint in the Bobruisk penal colony has left him with health problems that persist.
On December 13, 2025, he was released after another visit to Minsk by US President Donald Trump's special representative, John Cole, and taken to Lithuania.
