(written from a Production point of view)
The Vor'cha-class attack cruiser, making its debut in Star Trek: The Next Generation's fourth season episode "Reunion", originated from the strong desire of the The Next Generation's production staff to have a distinctive Klingon ship style of their own, as explained by Michael Okuda in 2009, "Those two ships–the Vor’cha and the Negh’Var–were an important part of the TNG evolution. They were the first Klingon ships in the TNG era that were not recycled from the feature films. As much as we love the battle cruiser and the bird-of-prey, we wanted very much for TNG to have a Klingon ship style of its own, and these ships gave it to us." 
The Vor'cha-class attack cruiser was designed by Rick Sternbach. According to Star Trek: The Next Generation - The Continuing Mission, Sternbach's design incorporated elements from the first Klingon vessel designed by Matt Jefferies for The Original Series. Sternbach himself noted in 2009,
"The Klingon Negh’Var class super battlewagon had its beginnings in the Vor’cHa class attack cruiser back in September of 1990, when the producers wanted a new main Klingon ship for the TNG episode ”Reunion.” The familiar D-7 type battle cruiser, even with its updated look from the Star Trek feature films, was getting perhaps too familiar, and I got the chance to come up with a new ship. The original design style of the battle cruiser was never far from my mind, since it was such an iconic Matt Jefferies creation, and I was always determined to provide some kind of lineage, some continuity, some evolution that viewers could recognize in the new hardware.
"On top of that, keeping Starfleet and alien styles distinct and interesting was what many believe set Star Trek apart from other SF productions. The Vor’cHa was great challenge and an opportunity to nail some specific bits of equipment, and add a little unofficial history to the Trek scenario. Before anything else, a big tip o’ the hat to Greg Jein and his minions for the terrific miniature.(...)The attack cruiser is a bit sleeker than the previous Bird of Prey, and less of a gritty dark green. It’s still armored and armed to the teeth, however, sporting a number of disruptor banks and torpedo launchers, as well as a new main disruptor cannon." 
Additionally, the Star Trek: The Next Generation Companion stated that the design of the Vor'cha-class ship was meant to illustrate the marriage of Klingon and Federation technologies due to the ongoing détente between the two powers, as further confirmed by Sternbach, "The structure, as well as the hull coloration, was meant to show a slight blending of Klingon and Starfleet technology, seeing as how there was something of a détente in operation" , and, "The idea here was to combine elements of the original battle cruiser (and the hyper-detailed versions from the movies) with some slight Starfleet influence, as though there was some deliberate technology sharing between the Federation and the Klingon Empire. The color was a bit lighter and less of a saturated dark green, the wing lines a bit curvier, but overall still recognizable as Klingon."  This translated in warp engines reminiscent of those of 24th century Starfleet vessels with the addition of Bussard collectors and a color scheme somewhere between the dark green of the Bird-of-Prey and the light gray of the USS Enterprise-D.
Sternbach intended the forward module of the Vor'cha-class to be an ejectable module in cases of emergency as evidenced by this blog entry in regard to his later Negh'Var-class modification, "I suppose the “daughtercraft” was an extension of the thing I did with the Vor’cHa with its main disruptor cannon section, in that it was detachable in a fight if damaged. I was influenced by the movie The Beast, which Richard James worked on, where one of the Russian tank guys said, “Out of commission, become a pillbox. Out of ammo, become a bunker. Out of time, become heroes.” Figured it would work for the Klingons. It wasn’t that the little ship was there to let them run away, but more to give them more options to stay in a fight. All a matter of what you do with the gear you’ve got." His intent, however, was dutifully transferred to the instruction sheet of AMT/Ertl's second TNG model kit of the Vor'cha, no. 6812, which stated that the forward part of the ship was a detachable mission specific module and interchangeable with other modules. In emergency situations it could act as a lifeboat. The model kit was designed as such, as the part was detachable. Even after the signing off on his final design, the forward module design of the Vor'cha-class, continued to occupy Sternbach's mind as he envisioned alternative design variations as late as January 1991, a solid two months after the episode was aired.
A set of four of Sternbach's original design sketches for the Vor'cha, was sold as Lot 292 , estimated at US$800–$1,200, in the Profiles in History's The Ultimate Sci-Fi Auction for US$850.00 on 26 April 2003. Two of Sternbach's forward module modification designs, were sold off as lot Lot 321 in the Propworx's Star Trek Prop and Costume Auction, estimated at US$100-$200, where they sold for US$120 (including buyer's premium) on 8 August 2010.
Physical studio model
The size Sternbach settled on was three-quarters of the length of a Galaxy-class, which was faithfully followed by Greg Jein, whose company built the studio model, and which came in at three feet, three-quarters of the length of the new four feet model of the USS Enterprise-D. Due to time restraints, Jein solicited the help of an acquaintance, David Merriman, Jr., who recalled, "A new Klingon ship miniature would be introduced in an episode where Worf learns of the existence of a bastard son. Anyway, in Greg's cover letter that accompanied the drawings, he explained that (surprise!–[remark: Merriman had made several more warp engines for Jein for previous models]–) they needed us to make the warp engine for that miniature. And (surprise!) time was a critical issue! Though possessing a great deal more surface detail than Federation warp engines, this one was at least symmetrical i.e. the left and right sides of the unit were of identical form. So, in the interest of time, I elected to make an intermediate master of only one side, make an in-house rubber tool and cast two sets (left and right half piece). A single winglet, wart and warp engine front assembly were made as well." (Sci-Fi & Fantasy Models, Issue 30, 1998, p.39) In the TNG Season 4 DVD-special feature: "Select Historical Data" (disc 7), both Sternbach and Jein are interviewed about the design and construction of the Vor'cha-class.
For its appearance in DS9: "The Way of the Warrior", the notion of a marrying of Federation and Klingon technology was partly reverted as the model was repainted from the light green color to the Klingon dark green with the raised hull paneling colored burgundy red, thereby being brought in line with the color scheme of the frequently seen Klingon Bird-of-Prey.
As of 2012, the studio model itself, never been modified, save for the paint adjustments, and having escaped the 40 Years of Star Trek: The Collection and It's A Wrap! sale and auctions, is still in the possession of Paramount Pictures and has been on tour displays such as Star Trek World Tour, Star Trek: The Exhibition and Star Trek: The Adventure as late as 2011. 
Other physical models
In Star Trek: Deep Space Nine' aforementioned fourth season episode "The Way of the Warrior", several other physicals models of the Vor'cha were also used for the massive battle scene, supervised by Dan Curry, Gary Hutzel and Glenn Neufeld. These were modified commercially available Playmate toys (No.6155) and AMT Star Trek model kits (No. 6812 ). (Cinefantastique, Volume 28, No.4/5, page 72) Being the first mass battle scene ever shown on Star Trek, it was also the last one entirely done with physical models (save for a few shots with a CGI Defiant, the only one available at the time). David Stipes repeated the procedure for DS9: "Call to Arms", using the same Playmate toys as before, the last time physical models of the Vor'cha were used.
Debris from an exploded Vor'cha-class breakaway model were sold in the It's A Wrap! sale and auction as Lot 18 on 29 December 2006 for US$1,025, having probably been used in a Star Trek: Deep Space Nine episode.
A limited run of 12, built from the same mold as the original studio model but without the internal lighting, was later sold, in 1997, at US$7,000.00 apiece with a certificate of authenticity signed by Jein at the Viacom Entertainment Store in Chicago.wbm The molds were later modified for the future Klingon attack cruiser seen in "All Good Things...", a design which, in turn, developed into the Negh'Var warship.
Sternbach's had his own personal AMT study model, as seen in the DVD special feature, auctioned off as Lot 294 , estimated at US$1,000–$1,500, in the aforementioned The Ultimate Sci-Fi Auction for US$800.
For appearances in later seasons of DS9, a CGI model was built at Foundation Imaging by Trevor Peirce, who gave his model the darker green color usually associated with Klingon ships, under the supervision of Ron Thornton, making its debut in DS9: "Sacrifice of Angels". (Sci-Fi & Fantasy Models, issue 32, 1998, p. 53)
the CGI model went on to make several appearances in and onto licensed Star Trek publications, most notably in the Star Trek: Ships of the Line calendars and their book derivative. In 2001, Robert Bonchune and Adam Lebowitz refined the model for representation in their book Star Trek: Starship Spotter.