They have been handed out free to every new mother in Finland since the 1930s, and have been credited with slashing that country's rate of sudden infant death syndrome (SIDS).
Now several hospitals in the US and UK are trialling baby boxes in the hope of giving all babies a healthy start in life.
But what is it about the free gift to new mums that is so special?
While the contents of the box includes just about everything you need for your new baby, such as clothes, nappies and perhaps a toy or book, it is the cardboard box itself that supporters say can save babies lives.
The box is intended to provide a safe sleeping space for babies up until they are eight months old. It comes with a firm mattress and usually a waterproof sheet and baby sleeping bag.
Babies can sleep in the box up to eight months old, and this is what is making the difference in infant mortality.
When introducing the baby box scheme to London's Queen Charlotte and Chelsea Hospital last week, Dr Karen Josh said it was hoped the box would reduce the risk of babies dying from SIDS or sleep related accidents by providing a safe sleep space.
"For too many years the UK has fallen behind its European counterparts when it comes to reducing infant mortality," she said, according to The Telegraph.
"These boxes and the education resources that sit alongside them have been proven to help reduce the infant mortality rate in Finland and we hope that these results could be replicated in the UK."
Meanwhile, the largest maternity care provider in Alaska began handing out baby boxes to all new mothers at the end to May. Manager of Providence Alaska Medical Centre's outpatient department Jen Aist said she had initially doubted how successful the trial would be.
"I did not think this would be as popular, but people have been picking them up with gusto," she told Alaska Dispatch News.
"The box doesn't do anything magical. There's nothing super-protective to the baby. But the box is an opportunity to reframe how we look at baby sleep space."
When Finland introduced the baby boxes in the 1930s, about 65 babies out of every 1000 died from cot death. That figure is now about 2 deaths for every 1000 babies.
Australian baby boxes
In Australia, like in most first world countries, the rate of SIDS has also fallen dramatically over the past two decades. Safe sleep practices have seen the number babies dying from sudden and unexplained death fall by 80 per cent since 1989 to about 115 per year.
Despite this improvement, some experts still believe the introduction of baby boxes in Australia would benefit new mothers, particularly those from low socioeconomic or disadvantaged backgrounds.
Founder of The Baby Box Co in Australia Edwina Lucas hopes that one day the government will adopt the boxes, and the education program that runs alongside them, as a mandatory gift to all new mothers.
In addition to selling boxes to people want to give them to friends as gifts, Lucas and her team work with corporate partners and community groups in a bid to reach mothers-to-be who are most in need.
"Our belief is that every baby deserves an equal start in life, regardless of their family's socioeconomic status," she said. "We hope the baby box together with the baby care education we provide access to can help achieve that goal."
Everything in the Australian Baby Box Co box has been chosen by early childhood experts and the sleeping surface meets stringent Australian safety guidelines.
"Our aim is to providing safe, quality baby boxes and infant care supplies to those families and babies that really need them most," Lucas said.