When paved roads and walkways were invented, they were a real step up from dirt roads. They stay rigid, no matter how much water or snow you dump on them, and, more importantly, they don't wash away.
So it might sound a little counterintuitive that the latest innovations in paving are permeable road and pavement surfaces which let water through. They're used to tackle two problems caused by the very impenetrability of traditional paving: large puddles and flooding, and ice formed when those puddles freeze.
So here's how it works: a material is used which allows water to permeate below the surface, rather than forcing it to flow into sewers and water runoff systems. The material usually also filters out dirt particles or leaves, so the water reaches groundwater level in a relatively clean state (though these can make the material less permeable over time).
One such material is permeable concrete paving, which normally looks a bit like this:
This diagram shows how the concrete channels water while trapping sediment:
Permeable macadam (a tarmac-like material) works in a similar way:
The system below is much simpler. A concrete overlay provides a firm surface for parking, but the surrounding grass allows water to seep directly into the ground.
Images courtesy of pavingexpert.com.
Of course, permeable surfaces mean these materials aren't as durable as traditional tarmac or concrete - roadways or walkways featuring these new materials are known as "low-impact", and it's doubtful they'd ever make it to motorways. Roads usually have a camber (a slight curve) anyway, meaning they're less likely to flood in the first place. Permeable paving is best suited to public squares or car parks: large areas of tarmac, asphalt or concrete where water tends to collect.
But there is an argument that more permeable roads are necessary to prevent flooding becoming a greater problem. As we cover ever-larger amounts of the world's surface with smooth, waterproof materials, existing drainage and sewer systems are forced to absorb more water year-on-year. A 2013 paper from the UK organisation Interpave ("the precast concrete paving and kerb association", obviously) estimated that surface water flooding causes around £270m worth of damage every year in the UK; and many floods are caused or exacerbated by overstretched drains. Permeable paving may well be a sustainable solution to this problem.