He is part of a Democratic political dynasty - his late father was also governor and hugely popular within the party. Many urged him to run (twice) for president but he refused.
His brother Chris is a primetime CNN anchor and he has interviewed his brother several times. One exchange they shared when he was sick with Covid was widely shared.
In the early days of the pandemic, Governor Cuomo was praised for steering his state from the worst-hit in the US to a success story.
And his near-daily press briefings in which he told New Yorkers the unvarnished truth about how bad it was made him a household name.
What are the Covid allegations?
In October, Mr Cuomo released a book, American Crisis, providing "leadership lessons" from the pandemic.
The book's summary describes the governor as "the standard-bearer of the organised response the country desperately needed" for the coronavirus outbreak.
But now he has been accused of holding back data about nursing home deaths.
The state attorney general released a report in January about New York's response to Covid in care homes and the handling of related data, saying it appeared a complete tally had not been provided to state lawmakers.
More than 15,000 New Yorkers in care homes have died since the start of the pandemic - believed to be the highest in the US.
But - until late last month - the state's health department had logged just over 8,500 fatalities.
The initial undercount was partly the result of a controversial policy to exclude residents that died outside of the care facilities, including in hospital, from the official numbers, according to a report.
Recently, Mr Cuomo acknowledged "a delay" in the reporting of some nursing home deaths but said that the overall Covid death count has always been accurate.
He said the failure to quickly answer questions from state lawmakers and the news media had created a void "filled with scepticism, and cynicism and conspiracy theories which furthered the confusion".
In February, in a private conversation leaked to the New York Post, a top aide to Mr Cuomo confessed to covering up the real numbers and withholding the information out of concern the data "was going to be used against us".
What are the investigations about?
Agents with the Federal Bureau of Investigation, as well as officials with the US attorney's office in Brooklyn, are looking at the way that Mr Cuomo has handled nursing homes and other matters related to the pandemic, according to reports.
In addition, some Democrats in the New York state Senate are hoping to take away his emergency powers. The lawmakers are likely to vote on a measure regarding his powers next week.
It is an unusual move by members of the governor's own party, a sign of the dire political situation he now faces.
What are the other controversies?
After Democratic New York Assemblyman Ron Kim criticised Mr Cuomo over the nursing home scandal, Mr Cuomo allegedly rang him and threatened his career.
Mr Kim accused his fellow Democrat of "verbal abuse" as other officials rushed to his defence.
In an interview with MSNBC, New York City Mayor Bill de Blasio called the account "classic Andrew Cuomo," adding that "the bullying is nothing new". The mayor claimed that many people across the city had received similar phone calls.
In late February, a former aide who had previously accused the governor of sexually harassing her while she was on staff published an essay detailing her claims. Mr Cuomo had denied the accusations when they emerged late last year.
In her essay, Lindsey Boylan accused Mr Cuomo of kissing her on the lips and asking her to play strip poker while on his private jet.
She also claims that he touched her without consent and frequently made inappropriate comments to her and other women about their appearances.
"As we said before, Ms Boylan's claims of inappropriate behaviour are quite simply false," a spokesman for Mr Cuomo said in a statement on 24 February.
Why does this matter to people in New York, and beyond?
Mr Cuomo became one of the nation's most influential Democrats during the early days of the pandemic.
His briefings, televised live, at times got more attention than appearances by the then-presidential candidate Joe Biden.
The controversy over the nursing-home deaths has created enormous political problems for Mr Cuomo, but he remains popular.
His poll numbers are good: 56% of those in New York rate him favourably, according to a recent Siena College survey. Analysts say he is a skilled operator, and still wields immense power.