Scientists are currently trying to make objects that do just this — they’re called ‘metamaterials’, and they have a very precise structure. Most materials we encounter on an every-day basis have a refractive index that’s greater than one — but metamaterials have a refractive index (for a particular colour of light) that’s *negative*. This ultimately just bends light the ‘wrong way’ when it enters a material, and it’s possible to use that bending to construct devices that act as an invisibility cloak.
To date, the only materials ever made with these properties bend light in the microwave end of the spectrum, not visible light — but they do work!
We’re a long way off having a convenient invisibility cloak, but we are getting there!