And on this latest outing - including a historical homecoming gig at Sheffield City Hall - it's easy to see why.
Keyboard wizard Martyn Ware and frontman Glenn Gregory dazzled with a spectacular lights and sound show that was second to none.
The all familiar thumping bass and avant-garde synth sounds, with Ware controlling the theremin, like some sort of musical sorcerer, was captivating.
Their timing, phrasing and delivery of some of the greatest sounds of the early 1980s wowed an enthusiastic crowd who took little persuasion to get out of their seats and roll back the years.
Amazingly, having played just about every venue in Sheffield, from the Leadmill to the roof on he Sheffield Hallam University building, they had never played a full concert at Sheffield City Hall.
And they had never toured with Ware's BEF studio production stars.
This really was history in the making.
But it was more than retro. The audience were not all mid-lifers who first fell in love to these sounds at the Crazy Daizy almost four decades earlier.
Pop icons Heaven 17 continue to appeal to new generations of fans, as they reinvent and align themselves with current trends, which has included performing with the likes of modern day electronic stars La Roux.
Here they were celebrating the 35th anniversary of their seminal debut album Penthouse & Pavement, which they played in its entirety in the first half of the show.
It wasn't, though, just a play through of the 1981 classic - they have cleverly reworked the tracks to breath new life into the work, which originally stayed in the top 100 for 77 weeks.
And connoisseurs in the building were not disappointed. This was a breathtaking reminder of one of the greatest albums of its decade, possibly of all time, which was born just a few hundreds yards away, where there is now a car park on the West Bar roundabout.
It was aptly called Monumental Studios, where the Dare album was recorded too at the same time by The Human League - also earlier founded by Ware, the now undisputed Godfather of electropop.
First track (We Don't Need This) Fascist Groove Thang is as relevant today as it was back at the start of the 1980s.
Next up the infectious title track, then Play to Win, which Heaven 17 did all night.
Geisha Boys and Temple Girls and Let's All Make a Bomb rubbed shoulders with the not so wel know, but equally enthralling Soul Warfare, The Height of the Fighting, Song with No Name and We're Going to Live for a Very Long Time.
Sheffield fans were then treated to a track Ware had specially chosen for the night - a reworking of the 1978 Human League song Being Boiled, credited by many as the song which sparked the electronic movement.
They also delivered their unique electro-pop take on You've Lost That Loving Feeling.
The second half of the show was a celebration of Ware's British Electronic Foundation - or B.E.F. - the name he gave to his studio work, which produced hits at the time for not just Heaven 17 but stars including Paula Yates, Billy MacKenzie, Sandie Shaw and most notably Tina Turner. It's mission strap line was Music of Quality and Distinction. And fans got that in abundance as special guests paraded on stage to belt out their greatest hits and covers.
Peter Hooton of The Farm was guest vocalist for a sing-along version of All Together Now, then a rousing version of Hillsborough campaign song, The Clash's Bankrobber.
Pop soul queen Mari Wilson sung her 1982 favourite Just What I Always Wanted followed by Rescue Me.
Sex Pistols punk rock legend Glen Matlock then thrilled with an electro rock version of his own Pretty Vacant followed by a feel-good cover of Pharrell Williams' smash Happy.
Gregory returned to sing Boys Keep Swinging in tribute to David Bowie - he's been touring with the Bowie band on The Man Who Sold The World tour and with Ware remembered seeing the late great star perform on the City Hall stage.
No Temptation? Fans had to wait for the penultimate slot - it was never in doubt. A Heaven 17 gig without their signature anthem would have been like Sinatra leaving out My Way.
Heaven 17's greatest hit was and will always be the showstopper. But it wasn't the usual finale.
In a fitting tribute to the late and sadly-missed new wave star Black - Colin Vearncombe - who died in a car smash earlier this year, the Heaven 17 boys and their special guests gave an encore of his 1987 international hit Wonderful Life.
A wonderful tribute to end a wonderful night.
HEAVEN 17 AND B.E.F. TOUR 2016 DATES
Thurs 20 October - Liverpool O2 Academy
Fri 21 October - Birmingham Town Hall
Sun 23 October - Glasgow O2 ABC
Mon 24 October - Gateshead Sage
Tues 25 October - Sheffield City Hall
Wed 26 October - Manchester O2 Ritz
Fri 28 October - Bury St Edmunds Apex
Sat 29 October - Basingstoke Anvil
Sun 30 October - London Shepherd’s Bush Empire
Also available are special VIP packages limited to 30 per venue including best seats, meet and greet with photo opportunity and a signed poster.