The arrangements - known as extradition - allow countries to make formal requests to each other for the return of suspects to stand trial for a crime in the same country it was committed.
The review was announced by the Home Secretary in September last year to make sure that the UK’s extradition arrangements work efficiently and fairly.
The panel is made up of three independent lawyers - Rt Hon Sir Scott Baker, a former Court of Appeal judge, David Perry QC and Anand Doobay.
The year-long review has looked in detail at the following five areas:
the Home Secretary’s discretionary powers to stop extradition
the operation of the European Arrest Warrant, which deals with extradition requests between European countries
where a crime is mainly committed in the UK, whether the person should be tried here
whether the US-UK Extradition Treaty is unbalanced
whether requesting countries should be required to provide sufficient evidence to prove an allegation
Responding to the report, the Home Secretary, Theresa May, said: ‘I am very grateful to Sir Scott Baker, Anand Doobay and David Perry for the work they have undertaken on this review. I will consider their recommendations carefully.’