In terms of combat efficiency and effectiveness, ranged weapons (especially kinetic ones or explosives) reign supreme. But there is a certain artistry in melee weapons, and value in their used for a lot of utility and some interesting things can be done with proficiency. Of these, the sword may be one of the more interesting and versatile melee weapons - unlike many others it does not necessarily evolve from a tool for working or hunting - but is a purpose built weapon to fight humans. This lends it a certain romanticism to the sword - which can be seen in the prevalence of swordsmanship both as a skill and sport in many parts of the Solar System.
Design-wise, fundamentally styles, patterns and types of swords remain unchanged, but in order to keep up with advanced in armor technology almost all of them utilize the "monofilament" style blade and advanced composites for sharpness and durability. While fabricators can mass produce swords, there is also something to be said for having them crafted specifically by those with knowledge and talent to do so - and quite a number who make swords are also capable of wielding them. The really daring can bridge into the exotic, utilizing vibroweapons and plasma swords.
Traditional swordsmanship sports persist in quite a few places, including forms of fencing in multiple styles and other HEMA groups on Venus, and the traditional kendo remains prevalent in several locations as well. Cultures with strong history have preserved historical martial arts schools related to the blade, taught for competition, self-defense and preservation of history. New arts and sports even arise, based on new weapons tech or cultural markers. Due to advanced in medical technology "blood sports" of all kinds can be popular in the system, and dueling in many forms has returned as a hobby sport, or even a way to settle disagreements. Numerous Extropian legal houses accept an honor duel as an appropriate way to settle a legal dispute.
These do not do as much to preserve the skills and utility of the sword as the concept of the "Street Samurai" however. Dating back to the 20th century, the idea of using swords as a weapon even when more advanced systems exist is kept alive in popular culture and seen as a marketable skill. Firearms may be restricted for safety or fabrication concerns, very few cultures are extreme enough to prevent a person from openly carrying a sword (in general public anyway). Restriction on longer weapons both by custom and practicality also occasionally makes smallswords, the Japanese daisho pair, and small parrying daggers or other accompanying weapons popular.
Carrying swords is intimidating, offering an air of danger but class to a person. It shows one is armed, and probably not afraid to fight - and that they have enough confidence to use a weapon which can require extensive training as opposed to an iron or a needler. Due to the ease of manufacturing and more common ability to carry this means many freelancers, hitters, troubleshooters and covert operatives train with various blades and may carry them to use - and some gangs focus entirely on utilizing blades thematically over guns (or perhaps, because they can get access to a pile of diamond axes). Additionally, the low-tech nature of a sword may make them preferable when faced with certain high-tech risks, as seen by use of Ultimate Purifiers and Rajput - an Exhuman neurode or TITAN puppet cannot backhack a katana.
Romanticism often turns to mysticism and urban legend, however. Many tales are told about the exploits of those who dare only to use blades. People still insist the classic "Zatoichi" tale of the blind swordsman is true. Legendary blade maker known by the alias "Masamune" is said to produce blades sharp enough to cut bullets like falling leaves - and a colleague (or possibly the same person with an alternate name) known as "Raikiri" can make blades which "cut lightning". And Alexandria the "Atomic Knife" is said to make a blade so sharp the right angle and force will cut an atom. Many have heard the urban legend of Annie Walker, who took only a blazing blue plasma sword into a camp of Martian bandits and killed every last one in revenge. One of the many skills the legendary operator "Jane Excalibur" has said to have mastered though countless lifetimes of forking and resleeving is use of a traditional longsword. While denied by the public media, the anarchist operator known as Thanatos once recovered an asset from Hypercorp hands in a daring highway raid vs Les Ghoules and Oversight armed with only katana and pistol. If you go to Phelan's Recourse, you might find Lou o' Light, who can teach you to cut the top off a small mountain in a single swing. And of course there are urban legends aplenty about hitmen who only fight with swords - such as the Night Cartel's Falconer M. or or the Triad's "101 Blades".