Roman engineers built thousands of roads throughout Europe and their Mediterranean neighbors of the Old World. The spice trade route in Southeast Asia is a trade route on an open sea. The silk road is mainly just a trade route on the Asian continent with only a few built roads. However in the New World, Native American Indians built roads throughout the Americas.
https://www.reddit.com/r/AskHistorians/comments/2n9qve/did_native_americans_make_roads/
Native Americans certainly made roads. There are of course, many different kinds of roads, ranging from simple footpaths to large, paved highways. I assume you're only interested in the larger, "formal" roads which we would recognize as such today.
One of the most impressive road systems north of Mexico is at Chaco Canyon. A massive network of built roads connects multiple archaeological sites in the region, fanning outward in a dendritic pattern from the canyon itself. The roads are quite impressive, in some cases they can be up to 9 meters wide. They're built up to go over dips in the landscape, and in places cut through hills much like modern roads do. The exact purpose of this road system (whether it's purely economic, political/militaristic, or ritual in function) is largely disputed, although it likely served a combination of such functions.
Within Mesoamerica, paved roads were quite common although they are usually restricted to within cities. Causeways were constructed through a gradient of materials, by placing large boulders on the bottom, slightly smaller stones on top of that, smaller ones on that, and gravel on top. In regions where lime plaster was available in sufficient quantity, the surface of these roads may actually be paved in plaster. In other areas sand or clay were likely used to top the roads off. Mesoamerican roads are very diverse, sometimes they conformed to the local topography, cutting switchbacks up steep inclines and winding around mountainsides. In other instances, like at Teotihuacan for example, roads formed a more rigid grid-like pattern that was imposed onto the landscape. While formal roads between sites were relatively rare in Mesoamerica, they were not unheard of. In the Aztec region, a maze of roads and canals cut through the capital city. Roads frequently formed causeways passing over bodies of water, and connecting islands to the mainland. A highly impressive road system can also be seen at the Maya city of Caracol, where a series of elevated limestone causeways connect the city to its satellite communities.
Of course, the most famous road system in the Americas were the Inca highways. The Inca created a road system that connected their capital to major centers throughout the empire. The Inca highways were often built up. Sometimes they were paved, but often they were made of packed earth. Suspension bridges allowed roads to cut across steep canyons and staircases were used to traverse steep inclines. What makes the Inca road system most impressive, however, is its scale. The Inca had a network of highways that essentially spanned the entire length of South America. The roads were used by state officials, and locals often needed special permission to use them. Storehouses containing food and supplies existed at regular intervals along most of the highway network, and could be used by messengers or other Inca officials for long voyages.
As for your other question, many of the roads I've described here are still around and you can go walk them today, but many are also overgrown and have fallen out of popular use.
But yes, Native Americans definitely had roads.
The Chaco Canyon culture in northwestern New Mexico built fairly impressive roads using impressive materials brought in from elsewhere and renowned for their straightness. Supposedly, they reached 180 miles long and 30 feet wide which has always seemed bizarre to me for that landscape and considering they didn't have carts, beasts of burden, or a particularly large population. For a number of reasons, it's believed the roads may have been largely ceremonial in purpose and not used for everyday travel or linking communities and resources.
The whole Chaco Canyon site is impressive and somewhat of a mystery still, if you ever get a chance to wander up there you should take a look.
https://www.desertusa.com/desert-trails/native-americans-trails.html
Major South-to-North Trails
At least three well-documented major south-to-north arteries – or, connected segments of trails – began in Mexico.
One, nearly 1200 miles long, started west northwest of Mexico City, at Guadalajara in the Mexican state of Jalisco. According to Sauer, it led westward for about 150 miles, to the Pacific Coast. It turned north northwest, following the coastline for nearly 500 miles. It turned generally north, paralleled the western flanks of Mexico’s Sierra Madre Occidental, crossed the border halfway between Nogales and Douglas, and continued across Arizona to the Zuni pueblos, a leg of some 600 miles. A second south-to-north artery, 1400 to 1500 miles long, began at Mexico City. It ran generally northward for more than 1000 miles across Mexico’s central highlands and through the Chihuahuan Desert basin to the Rio Grande’s Paso del Norte crossing. It followed the river upstream for about 400 miles to the upper drainage basin. These two south-to-north trails developed as avenues for trade, in effect, conduits for macaws, colorful feathers, copper bells and other Mesoamerican goods moving north and turquoise, obsidian, buffalo hides and other Southwestern goods moving south. Over time, the travelers from the south also introduced northern tribes to various ideas of religion and ritual; crops such as corn, beans and squash; the craft of pot-making; new products from distant workshops; and different concepts in architecture.
A third important south-to-north artery, more than 500 miles long, began in northern Chihuahua and Coahuila as a fan of trails with an apex at the Rio Grande’s "Grand Indian Crossing" in Texas’ Big Bend, at the southernmost point of the national park. It ran north, through basin and range country for 140 miles, veered generally eastward for nearly 40 miles to the Pecos River and an infamous ford called "Horsehead Crossing." It turned northwest for some 50 miles, until it struck the plains. It followed the southern and then the eastern perimeter of the Llano Estacado until it reached the headwaters of the North Fork of Red River, high in the Texas Panhandle. This trail, known as the "Comanche War Trail," summoned the Comanches and Kiowas, tribes of the southern plains, not to trade, but rather to plunder Mexican villages and haciendas, primarily for horses and slaves. Over time, the warriors of the plains returned home with so much booty that the Grand Indian Crossing resembled a "very wide, well beaten, and…much traveled thoroughfare...," according to Captain John Love, who attempted to navigate the Rio Grande by flat boat in 1850.
Unexplained Trail
While most Native American trails clearly accommodated the traveler, others served uncertain purposes, for instance, the enigmatic 400-mile network of "roads" which radiate from the famed Chaco Canyon Anasazi Puebloan complex, the early second millennium "Rome" of northwestern New Mexico. These roads, distinguished by long straight segments, unusual width (typically 30 feet), curbing, border walls, berms and small road-side "motels," usually connected Chaco Canyon – the region’s commercial and religious capital – with outlying communities. Some ended at the canyon rim, at precipitously steep stairways to the canyon floor.
Some archaeologists think that the Chacoan communities may have used the roads to distribute crops and other goods from areas with surpluses to areas with shortfalls, although that would not appear to explain the prodigious investment of manpower required for the construction and maintenance. Others have suggested that the Chacoans used the roads as tracks for foot races or as avenues for hauling construction timbers. Neither would that seem to justify the labor investment. Others suspect that the Chacoan peoples may have constructed the roads to function effectively as "stage sets" for elaborate pilgrimage processions and celebrations. If so, the commitment to religion and ritual would seem to be extraordinary. The Chacoan road complex will likely remain one of the mysteries of Southwestern prehistory. We can only say for certain that all the roads led to Chaco.
Native American Indian trails were sometimes marked by bending trees into trail markers
https://www.outdoorrevival.com/instant-articles/ancient-native-american-trails-marked-bending-trees-trail-markers.html
Native American Indian trails
Native American Indian roads in and around Chaco Canyon National Park
Inca Roads
Tenochtitlan causeways (raised roads), Aztecs
