We've looked at some of the claims being made.
Speaking at prime minister's questions, Mr Sunak was referring toofficial migration figures released on 23 November.
They show net migration of 672,000 people for the year to the end of June 2023.
That figure was up from 607,000 for the year to the end of June 2022, but down from 745,000 for the whole of 2022.
Net migration is the number of people arriving in the UK who plan to stay for at least a year, minus the people leaving for at least a year.
The Office for National Statistics, which released the figures, said "while it is too early to say if this is the start of a new downward trend, these more recent estimates indicate a slowing of immigration".
The figure is nonetheless at a historically high level - Mr Sunak has described it as "far too high".
The Conservatives' manifesto in 2019 promised that "overall numbers will come down". In the year that pledge was made, net migration ended up at 184,000.
Rishi Sunak criticised the Labour leader's plan to stop small boats coming to the UK.
Keir Starmer hassaid he wouldnegotiate a returns agreement with EU countries to send back some failed asylum seekers - if Labour wins power.
Mr Sunak's claim is based on an assumption that Labour would have to take 13% of all asylum seekers arriving in the EU as part of such an agreement.
The Conservatives have said this is because the EU has a policy of sharing asylum seekers between countries based on population size. They say this would mean the UK taking over 100,000 of them a year.
But although the EU has been discussing for years how to share responsibility for refugees, no deal based on population is in place.
Labour has said it would not - and could not - sign up to an EU quota scheme because the UK is not a member state, so any agreement would have to be outside that.
The prime minister was talking about small boat crossings.
He's made "stopping the boats" one of his five key pledges in government, whichwe've been tracking.
As at 13 November, 27,284 people had been detected crossing the English Channel in 2023,according to the Home Office.
At the same point in 2022, almost 42,000 people had been detected, so the number crossing is indeed down by a third.
Mr Thomas-Symonds - a Labour MP - was speaking on BBC Radio 5 Live after the Supreme Court's judgement on 15 November.
He was referring to an EU scheme - Dublin III - which allows member states to return failed asylum seekers to other EU countries, taking into consideration factors such as family reunion and irregular entry.
The scheme ended in the UK after Brexit in January 2021.
ButHome Office datashows the numbers involved were pretty small and actually more people ended up coming to the UK under this scheme than were removed in the final six years it was operating in the UK.
From 2015 to end of 2020, 3,961 people were transferred to the UK and only 1,763 were removed under the scheme.
Mr Rees-Mogg defended the government's Rwanda scheme on BBC Question Time on 23 November.
He said that the UN High Commission for Refugees (UNHCR) processes refugees in Rwanda. He argued the government's plan was "not that outrageous a thing to do, otherwise the UNHCR,which doesn't want the UK to do it, wouldn't be doing it itself".
It is true that the UNHCR,with financial support from the EU, has transferred refugees from Libya to Rwanda under a scheme called theEmergency Transit Mechanism (ETM).
However, the ETM is voluntary, not compulsory, like the UK's plan. The ETM offers vulnerable refugees, taken into detention by the Libyan authorities, a choice to have their application processed in Rwanda.
Libya - a major transit route for those hoping to reach Europe -is not considered a safe country for refugees.
People moved from Libya to Rwanda by the UNHCR are given assistance to resettle elsewhere should they choose to do so. It says that "as of March 2023, 932 refugees from the ETM centre have been resettled to Canada, Sweden, Norway, Finland, France, Belgium, the Netherlands and USA".
The prime minister was talking about the number of people who have been returned to other countries from the UK.
Mr Sunak did not make clear what type of return he was referring to, but the combination of voluntary and enforced returns this year does add up to about 20,000.
Thelatest datashows that 5,095 people were forcibly removed from the UK between January and October 2023. A further 15,204 left the country voluntarily in the same period.
About a fifth of the 20,299 people returned so far in 2023 were Albanians.
Not all of the 20,000 people returned were failed asylum seekers - some of them were foreign national offenders.
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The government has been defending its immigration policies after the release of high migration figures and the Supreme Court's ruling against its plan to send some asylum seekers to Rwanda.