On 7 April in 1983, American astronauts Don Peterson and Story Musgrave bravely stepped out of the space shuttle Challenger, the first time US space explorers had conducted a spacewalk in nearly a decade.
For about four hours, the men floated in the shuttle's exterior cargo bay while tethered to the spacecraft.
What they were wearing, at the time, represented a revolutionary departure from the custom-built, one-off spacesuits of the past.
Officially known as Extravehicular Mobility Units, or EMUs, these were two-piece, semi-rigid suits with 14 layers, designed to protect astronauts during extravehicular activity (EVA).
The suits included everything from communications gear to adult nappies and an in-suit drink bag.
Since that day in 1983, little has changed in the spacesuit fashion stakes.
The space agency's efforts to develop new improved spacesuits have had limited success. Nasa has already spent $420m (£310m) over 14 years without any significant progress, according to a report published this year from Nasa's inspector general.
"A flight-ready suit remains years away from completion," the report notes, adding that Nasa officials expect to spend a further $1bn (£740m) on design, testing, qualification and development efforts before two flight-ready suits are available for use.
The delay to spacesuits is likely to hold up Artemis, Nasa's programme to return to the Moon in 2024, the report adds.
In September, Nasa's Johnson Space Center called for private sector proposals for the new suits. They would be used for spacewalks on the International Space Station (ISS) and during future Artemis missions to the surface of the moon.
"Our undertakings in low-earth orbit, at the Moon and beyond, have evolved and are calling for innovative technology," Nasa deputy administrator Pam Melroy said in a statement.
"The next astronauts on the moon, including the first woman, will be kept safe in revolutionary spacesuits that fit better and enable greater human exploration than ever before."
Nasa wants industry help to build its new Exploration Extravehicular Mobility Unit (xEMU) and the Orion Crew Survival System.
The xEMU will mainly be for planetary spacewalks on the Moon, Mars and perhaps other bodies like asteroids, though it is planned to be modified for in-flight spacewalks.
It will have improved joints to give the astronaut more mobility, a new communications system and will have a rear-entry hatch.
The design will also be able to better fit astronauts of all sizes. In the past Nasa had problems finding spacesuits for smaller female astronauts.
The Orion suit is the suit crew will wear inside the spacecraft during launch and the return to Earth.
Proposals for the new suits are due on 1 December, with one or more contracts expected to be awarded by the following spring. Nasa plans a demonstration spacewalk with their newly developed gear as early as 2023.
"Nasa's investment in commercial spacesuits is another way that we are fostering a new lunar economy with private partners," Ms Melroy's statement added. "Similar to our partnerships in low-earth orbit, this endeavour will create jobs and help fuel an active economy at the Moon."
Tesla boss Elon Musk was quick to offer his help, tweeting that his company, SpaceX, "could do it if need be".
In an interview with the BBC, former Nasa administrator Sean O'Keefe says that he is not really surprised that the space agency has turned to the private sector for help.
"Every variant of every space suit Nasa has ever used was developed in concert with the private sector," explains Mr O'Keefe, who is now a professor at Syracuse University.
He added that Nasa's control over the performance requirements for the suit has largely been driven by the fact that only government-sponsored and trained astronauts have lived and worked in space and that has now changed.
"Now that the commercial space industry has demonstrated an ability to develop a space access transportation market, these companies will surely come up with new ideas on operational performance characteristics based on their evolving experiences," Mr O'Keefe says.
The current EMU model - which was only slightly upgraded in the 1990s - is specifically designed for spacewalks around the (now decommissioned) space shuttle and the International Space Station (ISS).
Among the few who have used a space suit at the ISS is Daniel Burbank, a former astronaut who in September 2006 logged a seven hour spacewalk at the station.
Mr Burbank explains that spacesuits have remained largely unchanged, primarily because of the fact they are now essentially "purpose built" for the ISS, which was launched in 1998.
"The design of the spacesuit is tuned and aligned to the needs of the space station," says Mr Burbank, now a senior technology fellow at North Carolina-headquartered Collins Aerospace.
"There are a lot of critical things that could happen to the outside of the space station that provides its habitable environment," he adds. "If those fail, we need to be able to get spacesuits on very quickly, go outside and make those changes."
As an example, Mr Burbank notes that the way the current EMU's gloves work with tools, the way the boots fit into portable foot restraints and even its size are all built with the ISS and space shuttles in mind.
In the future, however, new spacesuits will have to work for the US-led Artemis programme, which will return humans to the moon for the first time since the Apollo 17 mission in 1972.
For the Apollo moon missions several decades ago, each astronaut was given three tailor-made A7L suits: one for the mission, one for training, and one spare.
Made by ILC Dover, they had multiple layers to protect the wearer from heat, abrasion and micrometeoroids which could puncture the suit.
It was one of these spacesuits that Neil Armstrong was wearing during the Apollo 11 landing in 1969.
Current EMUs, Mr Burbank added, weigh over 150kg (23 stones), which even in the reduced gravity environment of the moon would likely be too heavy and unwieldy for this next generation of astronauts.
"A suit that would support the full range of crew members in a gravity environment on a non-engineered surface, we think has to look very different from the one we have at the Space Station right now," Mr Burbank says.
Both Mr O'Keefe and Mr Burbank believe that future spacesuit innovations will largely be driven by the private sector and the proliferation of commercial space missions in the future.
"The private sector is constantly developing a multitude of technology applications to stretch performance, efficiency, lower costs and improve quality," Mr O'Keefe says. "It's often a race against other commercial competitors for market share and brand recognition."
For Mr Burbank the experience of floating above the Earth in a spacesuit was one of the most rewarding aspects of his experiences in space - one he hopes that new space explorers will one day be able to share.
Mr Burbank remembers flying over the Himalayas at eight kilometres per second "like Superman".
"You don't want to come in. You want to stay out there as long as you possibly can, looking at the earth and all of its splendour," he says. "We want more people to have that experience."