The first amendments up for discussion to Clause One of the bill explore the role of the National Crime Agency (NCA) and put forward modifications to its operational and administrative functions.
Lords will then discuss a structure for NCA board membership and look at the Secretary of State's role supervising the board and the role of this board.
When members move on to debate Clause Two, the NCA's counter-terrorism function will come under the spotlight.
Last stage: Second reading
The Crime and Courts Bill had its second reading - the first chance for members to discuss main aspects of the bill - on Monday 28 May.
Lord Henley (Conservative) introduced the bill as the next stage of UK justice reform. He spoke about establishing the National Crime Agency (NCA) and its wider remit.
He explained: 'The National Crime Agency will... tackle serious and organised crime at the borders, fight fraud and cybercrime and protect children from sexual exploitation.
'For the first time, the agency will produce a single, authoritative intelligence picture on organised criminal gangs and their activities that will provide the basis for a co-ordinated national response.'
Following the minister, Baroness Smith of Basildon (Labour), asked for clarification on the timing and administration of the NCA. She said: 'I will raise the issue of governance and accountability of the NCA. Obviously, we want the NCA to be successful... However, there is a lack of clarity in some areas and there are also significant changes that require explanation and some justification from the government.'
Human trafficking then came under the spotlight when Lord McColl of Dulwich (Conservative) asked how the NCA would improve the UK's effectiveness in tackling this crime.
A former chairman of the Judicial Appointments Commisions (JAC), Baroness Prashar (Crossbench), spoke about selecting judges and the Lord Chancellor's role in ensuring diversity. She said: 'Promoting diversity is a joint endeavour between the JAC, the Lord Chancellor and the Lord Chief Justice.'
About the bill
The bill was introduced in the House of Lords at its first reading stage (formal introduction) on 10 May. It aims to establish the National Crime Agency and suggests abolishing the Serious Organised Crime Agency and the National Policing Improvement Agency.
It also examines the structure, administration, proceedings and powers of courts and tribunals and addresses issues like border control and drugs and driving.
What is committee stage?
Detailed line by line examination of the separate parts (clauses and schedules) of the bill takes place during committee stage. Any member of the Lords can take part.
It usually starts no fewer than two weeks after the second reading and can last for one to eight days or more.
The day before committee stage starts, amendments (changes) are published in a marshalled list – in which all the amendments are placed in order. Amendments on related subjects are grouped together and a list (groupings of amendments) is published on the day.
During committee stage every clause of the Bill has to be agreed to and votes on the amendments can take place. All proposed amendments can be discussed and there is no time limit – or guillotine - on discussion of amendments.