In the world of vintage watches, it’s not uncommon to come across the rare and unique. Spend a little time looking, and you’ll come across limited edition models, one-off complications, and feats of innovation that all, in one way or another, seem to exemplify the craft of watchmaking.

More difficult is to find the unusual — the striking timepieces that push the boundaries of convention and can turn the heads of even the savviest of collectors. These are the true rarities, made by luxury watchmakers with unlimited budgets and access to some of the world’s greatest and most creative minds.

Here are four of those such watches. As you can imagine, they also happen to be some of the most expensive ever produced.

Richard Mille RM 56 Sapphire

Any one of Richard Mille’s creations would make the list, but the one that has to take the crown is the Richard Mille RM 56 Sapphire.

Richard Mille RM 56 Sapphire

Valued at around £1.2 million, the RM 56 is unusual and unique due to its entire case — front bezel, caseband, and back bezel — being cut and milled from solid blocks of sapphire. This is what gives the watch its transparent appearance — a look which some critics believe is too close to plastic. But whatever your tastes are, with aerospace nanotechnology on the outside and an innovative cable and pulley system under the hood, it can’t be denied that the RM 56 is a work of unrivalled beauty and engineering.

Patek Phillipe Sky Moon Tourbillon 6002G

With its 18k white gold case and stellar illustration of the northern sky, the Sky Moon Tourbillon is one of the most recognisable Patek Phillipe watches ever made.

Patek Phillipe Sky Moon Tourbillon 6002G

The 6002G is one of only two watches to feature extravagant and incredibly detailed engraving around its face. This creates a worthy surround for the main show: the time, perpetual calender with retrograde date, indications for sidereal time on a 24-hour scale, and angular progression and phase of the moon. The watch manages to pack all this in due to its unusual double-sided dial. And if that wasn’t enough, to justify its cool £1.1 million price tag, it will also chime the hour with two cathedral gongs.

Patek Phillipe Reference 2523 World Time

Made at a time when flying around the world was less of a commonality, at its release, the Reference 2523 World Time watch was less practical than it was, you guessed it, unusual.

Patek Phillipe Reference 2523 World Time

Using an ingenious disc-system invented by Louis Cottier in 1931, the watch displays the time of prominent locations around the globe. And in this version of the watch, it does so with a hand-painted map of North America as its background. Sold for around £2.2 million at auction, today the Ref 2523 is highly prized among collectors.

The Jacob & Co. Astronomia Solar

A unique timepiece that combines the craftsmanship of Swiss watchmaking with the flair and creativity of the decorative arts, the Jacob & Co. Astronomia Solar is one of the newest, yet most distinct watches on our list.

The Jacob & Co. Astronomia Solar

Stealing the show at Baselworld in 2014, the $1 million watch features a miniature rendering of the celestial world, with every element in constant motion. Over three dials, the watch also shows the time, the tourbillon, and a tiny globe that represents the Earth. Its pièce de résistance is a 1.5 carat citrine with 288 facets, which sits at its centre.