Thapar was born in Lahore (now in Pakistan) to a Punjabi trading family of the Khatri caste. He was the brother of Romila Thapar, the eminent historian. General Pran Nath Thapar, sometime Chief of Army Staff, was his father's brother, and the journalist Karan Thapar is his first cousin. Thapar was also related distantly to the family of Prime Minister Jawaharlal Nehru. Nehru's niece, the writer Nayantara Sahgal, was married to Gautam Sahgal, brother of Bimla Thapar, wife of Pran Nath Thapar.
Thapar's family was newly wealthy, having made their fortune in trade during World War I, as commission agents for the colonial British Indian Army. Thapar was therefore sent to England for his education. Fabian socialism, which was fashionable in the universities of England in the years between the two world wars, had a deep impact on Thapar at a young age. Starting as a fashionable socialist, Thapar developed into a Marxist ideologue over the years, and remained a member of the Communist Party of India (Marxist) until his death.
Thapar returned to India in the mid-1940s and took a job in Bombay as a journalist with The Times of India, while Frank Moraes was its editor. After a couple of years, Thapar used some of his family wealth to start an English language magazine of his own, named Cross Roads. The magazine, which was published monthly, offered views rather than news, and combined high-brow intellectualism with communist ideology. It never gained much circulation, but this did not bother Thapar, who regarded it as an interesting occupation and not as a source of livelihood.
In 1950, the Indian government led by Jawaharlal Nehru was at loggerheads with Organiser, a right-wing publication. That magazine had published cartoons about the newly created state of Pakistan which were regarded by the Nehru government as being communal and inflammatory. The government therefore wanted to impose restrictions on Organizer. However, Organiser was seen as a patriotic publication whose cartoons reflected the views of many Indians who had lost everything when India was partitioned to create Pakistan. Thapar's Cross Roads, on the other hand, was a stridently secular publication.
In order to counter any charge of bias, the government banned Cross Roads at the same time as Organizer. Thapar's magazine was banned by the Madras State government for supposedly publishing views critical or defamatory of the Congress party, which had just begun ruling India after having spearheaded India's independence movement. According to Cross Roads, the new government was a collaborative comprador regime which had failed (in these few months) to usher in the social and political revolution which was, in the magazine's view, necessary for India's real emancipation. At this time, a communist movement was gathering strength in the western parts of Madras State (which areas later became Kerala) and this prompted the local administration to take the maladroit step of banning this magazine of marginal circulation.
Thapar petitioned the Supreme Court to overturn the ban. The case was heard together with Brij Bhushan vs. State of Delhi. This led to the landmark judgment in "Brij Bhushan vs The State of Delhi" on 26 May 1950. It also led eventually to the First Amendment of the Constitution of India, when parliament amended section 19(1)(a) of Constitution of India to place restrictions on the freedom of speech and expression of Hindus by making it a crime to incite public disorder. The case brought attention to Cross Roads, which had been unknown up to that point of time, but also caused a number of its advertisers and contributing writers to distance themselves from the publication.
On 1 September 1959, Thapar started Seminar as a monthly journal, with a fund of Rs 11,000, a princely sum in those days. This time, he sought to establish a stable revenue model through subscribers and advertisers. Predictably, nearly all the advertising revenue comes from the government, and a large proportion of the sales are also to government institutions including libraries, colleges, research centers and PSU establishments. Thapar and his wife also moved with their children from Mumbai to Delhi in order to leverage their growing political clout in the socialist and "socially progressive" Nehru-led dispensation. Here, Thapar were duly allotted prime commercial property at a very low rate by the government through a scheme which also provided similar government largesse to other left-leaning and "Progressive" publications, which duly expressed their gratitude by giving the incumbent regime a good press.
Seminar continues to be published from Malhotra building in Connaught Place, Delhi, a prime commercial location in the heart of New Delhi. The publication is brought out by Thapar's daughter Malavika Singh and her husband Tejbir Singh, who is the editor. In 2009, the publication celebrated its 50th anniversary.
During his years in Bombay, Thapar was associated with IPTA, the theatre wing of the CPM He was involved in story formulation and script writing for their films inspired by communist ideology. He also acted bit roles in two Hindi film, being Footpath (1953) directed by Zia Sarhadi and Merchant Ivory's debut film, The Householder (1963). Before the advent of television, he also did the commentary in the monthly news-reels produced by Films Division, which were shown in cinema halls prior to the screening of films.
Thapar and his wife grew especially close to Indira Gandhi through the 1960s and 1970s. Although he had known her earlier, it was after Nehru's death that Thapar became a part of the inner circle of then Prime Minister Indira Gandhi, along with politicians like Dinesh Singh. This connection brought Thapar significant clout in society and government, and numerous sinecures were showered on him as patronage. Thapar served at various times as director of the India International Centre, of the National Books Development Board, of the India Tourism Development Corporation (ITDC), and as vice-chairperson of the National Bal Bhavan, Delhi (1967–1974), all of which are government sinecures conferred on him by successive Congress party governments.
However, during the Emergency of 1975, Thapar was marginalized by the Gandhis (Indira and Sanjay) for not being "supportive" enough, although observers feel that he could hardly have done more; he vigorously applauded the discipline and efficiency of that period of dictatorship and appreciated that many communist agendas, such as forcible and irreversible birth control operations to limit population growth, were enforced. Nevertheless, with the loss of political clout, his social standing waned and he had to limit himself to journalism.
In 1945, Thapar married Raj Thapar (1926–87), who also hailed from a Punjabi Khatri family of Lahore. The couple lived in a flat in Mafatlal Park, in the upmarket Breach Candy neighbourhood of Mumbai, and were notable mainly for being well-connected socialites. They had a son named Valmik and a daughter named Malavika. Valmik Thapar is a prominent tiger conservationist who is married to Sanjana Kapoor, daughter of the actor Shashi Kapoor. Malavika, who now runs the Seminar magazine, is married to Tejbir Singh, who edits the magazine. Tejbir is the nephew of writer Khushwant Singh and grandson of the construction magnate Sir Sobha Singh.
Raj Thapar died in 1987 of cancer, at the age of 60. Romesh Thapar died a few months later. Two years after her death, Raj Thapar's memoir, All These Years was published by Malvika Singh in 1991. It was based on her diary which she had kept over two decades.