Donald Trump has addressed the Republican National Convention in Milwaukee, accepting the nomination as the party’s presidential candidate.

His speech – which lasted one and a half hours – contained plenty of claims about his record as president versus Joe Biden’s.

BBC Verify has been checking some of them.

CLAIM: “Our crime rate is going up, while crime statistics all over the world are going down”

VERDICT: Violent crime in the US fell last year.

Mr Trump did not specify what kind of crime he was talking about.

Violent crime was down 6% in 2023 and there was a significant drop of 13% in the murder rate, according to preliminary FBI data.

These statistics aren’t a complete picture as some local police departments have not yet submitted their figures. The official FBI figures for last year will be released in October.

The latest FBI crime data, which is also preliminary, indicates this downward trend in violent crime in the US has continued into 2024, with reported incidents falling 15% in the first three months of this year, compared with the same period last year.

Recorded murders dropped by more than 26% in the same time period, according to the figures.

CLAIM: “We’ve had the worst inflation we’ve ever had under this person [Biden]”

VERDICT: Under President Biden, inflation reached around 9% before falling to around 3%. That’s nowhere near the worst in history – the record was 23.7% in 1920.

Inflation rose significantly during the first two years of the Biden administration, hitting a peak of 9.1% in the year to June 2022.

This was comparable with many other Western countries, which experienced high inflation rates in 2021 and 2022, as global supply chain issues as a consequence of Covid and the war in Ukraine contributed to rising prices.

But some economists say Mr Biden’s $1.9tn (£1.5tn) spending plan in 2021 was a factor as well.

Since then, US inflation has fallen steadily with the latest monthly figure at 3% as of June.

Mr Trump also said “we had no inflation” under his administration.

When Mr Biden came to office in January 2021, inflation was low – at 1.4% – but prices were still rising.

CLAIM: “Our opponents inherited a world at peace”

VERDICT: There were dozens of conflicts globally in the last year Mr Trump was president, according to experts.

Mr Trump followed this claim by saying the world was now a “planet at war” and he highlighted the current conflicts in Ukraine and Gaza.

He’s right that they didn’t happen on his watch but he’s wrong to claim that he left “a world at peace” to President Biden.

In 2020, the last full year Mr Trump was President, there were 56 active conflicts around the world, according to the Peace Research Institute in Oslo.

It classed eight of these as wars, including ones in Syria, Afghanistan and Yemen.

CLAIM: “If somebody wants to buy a gas-powered car or a hybrid they are going to be able to do it, and we’re going to make that change on day one”

VERDICT: The implication here is that Americans cannot buy these cars or will not be able to. There is no current ban on vehicles which run on gas (petrol) in the US and Mr Biden has not set out a plan to introduce one in the future.

In March, the Environmental Protection Agency announced new emission standards for cars built between 2027 and 2032.

It estimates the car industry could meet these standards if 56% of new vehicles are electric by 2032.

The Biden administration has said this is not a ban and new petrol-powered vehicles can still be sold beyond 2032.

CLAIM: “The jobs that are created [under Biden] – 107% of those jobs are taken by illegal aliens”

VERDICT: We can’t find any evidence for this figure and the data shows millions of new jobs have gone to US-born workers.

The US Bureau of Labor Statistics produces figures for both US-born and foreign-born workers.

But it does not have a separate category for illegal immigrants and Mr Trump did not say where he got his figure from.

Since President Biden took office in January 2021, the number of US-born workers has increased by 7.8 million.

Over the same period, the number of foreign-born workers in the US rose by 5.5 million.

CLAIM: “The biggest tax cuts ever”

VERDICT: As President, Donald Trump did bring in big tax cuts but they weren’t the largest in history.

Mr Trump’s Tax Cuts and Jobs Act of 2017 brought in sweeping cuts to taxation across the board. These are due to expire in 2025 unless the next administration extends them.

According to analysis done by the independent Committee for a Responsible Federal Budget, Trump’s tax cuts were the eighth-largest since 1918 measured as a percentage of the size of the economy (GDP), and the fourth-largest in dollar terms since 1940 adjusted for inflation.

Although, Mr Trump didn’t introduce the largest tax cut overall he did pass the largest corporate tax cut in US history.

The 2017 law reduced this tax rate from 35% to 21%.

That was more than the cut passed under Ronald Reagan in the 1980s, which lowered the rate from 46% to 34%.