On paper, this machine is daunting: A “hand-crafted” 4.0-liter twin-turbo V-8 tuned to 577 horsepower and 627 pound-feet of torque; every technological trick in Mercedes-Benz’s considerable toy chest; and, gulp, an all-in price tag much closer to $200K than $100K. Approach with caution!

But no. This AMG Monsterwagen is dead easy to drive (if not to operate to its fullest), supremely comfortable (once everyone’s clambered up into it), astonishingly agile and downright useful. It’s a friendly errand-runner, beach wagon, tow truck and off-road paragon that’s also (after hosing away the mud) just the thing to convey two couples in style to the opera for a black-tie opening night.

Of course, with this throbbing volcano of an engine and the adjustable/programmable AMG gear plus all-wheel drive, 22-inch forged wheels and high-performance tires, it is also a speed sled that defies all SUV norms. And, finally, the renowned G-wagen, the Geländewagen, is the last word in automotive cool. Ask any Russian oligarch, Arab sheik or Beverly Hills divorcee. Or even my six-year-old granddaughter.

Geländewagen is German for “cross-country vehicle.” If it looks like something that escaped from a military motor pool, it is. Its genesis goes back to the mid-‘70s, when the Shah of Iran asked for 20,000 Jeep-like carryalls for his troops. Not only was this a staggering order, but the Shah (or maybe Iran; they were more or less the same thing then) was also a major stockholder in Mercedes-Benz. The company snapped to attention, clicked its heels and barked, “Sir! Yes, sir!” or, more likely, “Jawohl, mein Herr!”

Perhaps in a mild panic, M-B turned to a corporate cousin in Austria, then called Steyr-Daimler-Puch, builder of the legendary Pinzgauer 4- and 6-wheel-drive military vehicles. The Austrians got to work designing and testing prototypes in boondocks all over the world. But by the time the G-Wagen was ready for delivery, in 1979, the Iranian Revolution had deposed the Shah. There goes that order.

Not to worry. Other militaries and police, fire and rescue units around the world put their hands up for the vehicle. Meanwhile, Land Rover had spawned the luxury off-roader market with the Range Rover and Toyota was following suit with ever more deluxe versions of its Land Cruiser. Mercedes-Benz saw the trend and began to dress up the G-Wagen for civilians, too. Untold variations and limited editions—each crazier, more powerful, luxurious and spendy, some with six-wheel drive and all still made in Austria—have appeared since.

It was only natural that AMG, M-B’s tuner division, would also contribute to the G-Wagen madness, in the past with twin-turbo V-12 engines. The current version, this one, with a (slightly) more fuel-efficient V-8, may be the best one yet because by now M-B has fully sorted out how to make something so tall, heavy and un-aerodynamic behave not just in the rocks and sand and on Rodeo Drive, but also on the autobahn at speed. Drivers have an army of sensors, actuators, computers and software, some of which did not exist until relatively recently, to thank for this.

As a professional nitpicker, I must point out the vestigial running boards, which are almost too narrow to be useful; the vintage door latches, inside and out, that seem to stump everyone at first; and the gear selector, a puny stalk on the steering column that one might mistake for the turn-signal lever. (A G-Wagen, particularly the AMG version, deserves a mil-spec floor-mounted stick shift done in unobtanium and leather.)

The G-Wagen we’re driving is a 2021 model, but no matter—about all that’s changed in a year is the price. An “ordinary” G-Wagen, the 416-horsepower G550, starts at $131,750. The AMG G63 presently lists for $156,450. Our example, with the fancy steering wheel, the 22-inch rims, the blacked-out Night Package and the “Manufaktur” interior, comes to $172,300. A special price for a special vehicle. After a week on the throne, it’s easy to see why people fall in love with these things.