Move over classic round watches. The shape of things to come seems to be more sharp edges than gentle curves.

And the humble watch part making it all happen? The bezel, the piece that rings a watch’s dial and holds the protective crystal glass in place.

In line with the continuing popularity of luxury sport timepieces, brands are increasingly asking for metal sport designs with faceted bezels, said Eric Giroud, a Swiss watch designer who has worked with more than 60 brands. And the requests, he said, often cite the Audemars Piguet Royal Oak and the Girard-Perregaux Laureato, both of which have octagonal bezels.

“They’re seen as icons and very successful models,” said Mr. Giroud, who added the Royal Oak is especially “appealing because it has a very strong identity and there is a very nice coherence with the whole of the watch elements.”

This year marks the 50th anniversary of the Royal Oak, and the introduction of commemorative designs began in January with the gold 39-millimeter Royal Oak Jumbo Extra-Thin with dial finishes like smoked gray and yellow gold (price on application).

“The intention of watchmakers in the 1970s was to make something stand out,” said Clémence Dubois, chief product and marketing officer at Girard-Perregaux, maker of the Laureato (which first appeared in 1975 and was reintroduced in 2016 for the house’s 225th anniversary). “So playing with different elements was very important in ensuring the watch was recognizable and could speak for itself.”

The Laureato features a round dial within an octagonal bezel, all set on a round case, with alternating brushed and polished finishes for further contrast. This interplay of shape and texture really makes the bezel facets pop, Ms. Dubois said, especially when compared with conventional round watches.

But because the dial is round, the wearer has a tendency to forget about the octagonal bezel so, she said, the designer has to come up with tricks, like the alternating finishes, to highlight the octagonal effect.

Girard-Perregaux has continued to present new Laureatos each year, most recently the chunky 44-millimeter Laureato Absolute Gold Fever in titanium ($17,900), introduced in November.

Also looking to the 1970s is Zenith, which in January revisited its first Defy model in the Defy Revival A3642 ($7,000). The watch’s octagonal case has a 14-notch bezel, with the contrast between the facets further offset by the unusual square hour markers and chunky hands, all set on a brown gradient dial. It followed the titanium Defy Extreme Desert ($22,000), introduced last fall, which had a 12-sided bezel handcrafted from falcon’s eye, an unusual blue-gray semiprecious stone that also appeared on the watch’s pusher protectors.

But not all faceted designs are revival stories: Seiko recently refashioned its round, solar-powered Astron GPS Solar as an angular polygon, complete with a matching bezel, while the new G-Shock GM2100 featured a slim octagonal case and bezel. In January, Hublot unveiled additions to its Sang Bleu collection, with cases and bezels in ceramic and gold that were sliced, carved and beveled into alternating hexagons, rhombuses and triangles.

And the independent watchmaker Romain Gauthier — who has built a reputation for painstakingly chamfering, or beveling, his designs — recently introduced the Continuum in titanium (at $42,550, significantly less expensive that his other timepieces). The watch’s bezel was machined into a circular bevel and then faceted with six indentations, each one hand polished to create contrast with the bezel’s satin finish. The same process then was repeated on the back of the watch, an effort that he described as “purely a question of design.”

Mr. Gauthier said it took time to perfect each facet. “The facet design depends on the shape and design of the chamfer,” he said. “The facets don’t touch — and my thinking was to play with different levels of finishing.”

The bezel was polished by hand — a welcome contrast to machine polishing that often looks too hard and perfect, Mr. Gauthier said. “You see some curves and it’s not perfectly sharp. In the end, I think people love that.”

While faceted bezels have an aesthetic appeal, some brands are focusing on their functionality, particularly to improve the grip on divers’ watches. In November, Tudor, a longtime supplier to the French Navy, unveiled the technical diver watch Pelagos FXD ($4,450), developed with the French Navy’s combat swimmers, and whose 120-notch, bidirectional bezel was designed for optimal underwater navigation.

TAG Heuer’s key reintroduction last year was an ergonomic nip-and-tuck on its Aquaracer diver, which led to more tactile fluting on the 12-notch bezel, a treatment the brand first introduced in 1995. And the Aquaracer Professional 200 collection (from $1,950), which debuted in January, slimmed cases down to 40 and 30 millimeters from 43 millimeters, the size used last year. The collection now is being marketed as all-terrain watches for extreme sports.

Tactility and precision were the starting points for the military watch brand Vertex, which in December unveiled its first diver ($3,250), with a bezel inspired by the rear sight adjuster on a World War II Bren machine gun. “They’re designed as easy to grip and easy to turn, which is exactly what you want for a bezel — especially a movable one,” said Don Cochrane, the brand’s founder, who used the sight adjuster’s spacing and distinct knurling design to create the M60 AquaLion’s scalloped edges and gripping pattern.

Despite their rugged, tough styling, notched bezels can be feminine, too.

Bulgari recently unveiled the first women’s model of its faceted Octo collection, the skeletonized Octo Roma Tourbillon Lumière (price on application), offered in a compact 38-millimeter case and set with 239 diamonds totaling 12.5 carats.

And eight asymmetrical facets anchor Dior’s Gem Dior watch collection, which riffs on the shape of rough gemstones. A new model ($77,000) with an aragonite hard stone dial is ringed by a diamond bezel featuring a single slice of carnelian, a dark red semiprecious stone, highlighting the watch’s multifaceted beauty.