Junior Isas, which aim to encourage people to get into the savings habit from a young age, reach their fifth birthday on Tuesday.
The children's savings accounts, sometimes called Jisas, are open to people aged under 18 and living in the UK.
They were launched on November 1 2011, as the successor account to Child Trust Funds (CTFs).
Official figures show around 700,000 Junior Isa accounts were opened in the 2015-16 tax year.
Parents or guardians can open a Junior Isa and manage the account, but the money held there belongs to the child.
Funds are "locked in" until the child reaches 18, when the account becomes an adult Isa by default and the cash held in it remains ring-fenced from the taxman.
There has already been some evidence that Junior Isas are helping young people to get into the savings habit - and that they are being responsible with their money.
According to financial services firm Hargreaves Lansdown, 90% of its maturing Junior Isa accounts continue to be invested when the holder reaches 18, rather than being cashed in.
Danny Cox, a chartered financial planner at Hargreaves Lansdown, said: "It's encouraging to see the vast majority of people retaining their Isa savings from age 18 showing that people can be trusted with money at a relatively young age."
Rachel Springall, a finance expert at Moneyfacts.co.uk, said providing a savings pot for a child's future could give them a helping hand with university expenses and getting on the property ladder.
She said: "It's easy to start saving for a child as a Junior Isa can be taken out and matures into an adult Isa when the child turns 18.
"Parents will need to do this, but then grandparents can contribute. Savers can choose a cash interest option or a stocks and shares, which in the long-term is likely to outperform the low interest rates on offer today."
Ms Springall said the top-paying Junior cash Isas are offering interest of as much as 3.25%.
She said: "Coventry Building Society currently offers a 'best buy' deal paying 3.25% and accepts transfers in - just keep in mind that this is a variable rate so it could change over time."
Up to £4,080 can be saved into Junior Isas in the current 2016-2017 tax year. Children cannot hold both a Junior Isa and a CTF at the same time. If parents want to open a Junior Isa for their child they must ask the provider to transfer the fund into it.
Jason Hollands, managing director of Tilney Bestinvest, said some parents may still be wary about their offspring being able to access large sums of money when they reach 18.
He said: "Therefore, parents should consider using their own - now sizeable - Isa allowances instead and use the funds to settle specific costs, such as college fees, as they arise or gift money to their children when they feel it is appropriate. Jisas are a potentially useful allowance but not the only option for saving for children."
Jane Ellison, Financial Secretary to the Treasury, said: "Junior Isas have made it easier than ever for parents and grandparents to save for their children's future, and the 730,000 accounts saving £1,248 each on average in the last year alone are testament to their success."