Don’t envy Lowery Stokes Sims, the curator of the Museum of Arts and Design in Manhattan, her many recent trips to Latin America. As the force behind New Territories, the museum’s survey of recent design in 14 countries (through April 6), Sims maintained a punishing schedule of studio visits; her itineraries and notes are viewable on iPads in the museum’s ingenious “Curator Lab.” Sims discovered many more worthwhile items, most of them by young designers, than the museum had room for.

Her other challenge was finding a way to organize hundreds of objects that defy easy categorization. They range from efforts at what she calls “upcycling” (for example, chairs made from steel drums by Venezuelan artist Rolando Pena) to traditional crafts given contemporary twists (such as rugs decorated with QR codes, by Chilean artist Guillermo Bert, in collaboration with various weavers). Then there are artworks with political overtones. The Peruvian artist Lucia Cuba, for instances, makes dresses dedicated to the victims of that country’s forced sterilizations.

Sims’s choice was to organize the show both geographically and topically, first choosing cities she considered important incubators of design, then assigning each city a theme. The Havana portion of the show, for example, is titled Navigating Personal and Civic Space; it includes Ernesto Aroza’s striking photos of old buildings rejiggered for new uses. But there are also pieces from Brazil, Argentina, and Colombia displayed under the Havana rubric.

The layering of themes onto places results in pigeonholing. Caracas, for example, is shown as the height of sophistication (the display of furniture based on the work of Werner Panton and Ettore Sottsass could be in a high-end showroom), while Oaxaca, Mexico, is represented by, essentially, a roadside craft stand. Sims, asked about the problem, says, “We’re not stereotyping. We’re just reporting on what’s out there.”

True. And, anyway, it’s hard to imagine how else she could have organized such a wide range of material. Which is why one almost longs for the days when a design museum could display beautiful objects, without having to come up with elaborate themes and theses. Must an exhibition always be a dissertation?

Somewhat troubling is the plethora of decorative items made with guns and ammunition. They include the Bulletproof Side Table, decorated with shell casings, by the Monaco-based Brazilian designer David Elia; and a section of a fence topped by realistic toy guns, by the Brazilian architects Isay Weinfeld and Marcio Kogan. More conceptual art than design, these pieces reflect the preoccupation with violence among upper class Brazilians. Sims, who was surprised by the preoccupation, sees the artworks as a kind of exorcism.

It’s a testament to Sims’s talent at identifying up-and-comers that, in the opening days of the show, a number of New York dealers visited the museum, hoping to discover the next Vik Muniz, the Brazil-and-Brooklyn based art superstar, or Campana Brothers, the renowned Brazilian furniture designers. They may well find them in this sweeping and rewarding exhibition.