Why haven't we started exploring the Asteroid Belt?

note: Dan B submitted his excellent answer while I was still drafting mine but I'll let mine stand anyway because mine has a picture.) NASA's Dawn Mission has visited asteroids Vesta and Ceres (still there in fact). read more

JAXA’s Hayabusa 1 probe visited Itokawa 25143 in 2005 (an Apollo Earth/Mars crossing asteroid) and returned dust samples, and Hayabusa 2 will visit Ryigu 162173 in 2018 (Apollo asteroid). NASA just announced a mission to Psyche and Lucy, both metal-rich, in Jupiter’s Trojans asteroid family. read more

We do not yet have the technology to reach the asteroid belt and return. Probes that have gone to or beyond the asteroid belt are multi hundred million dollar devices. It is a technology that is still quite a long way in the future. read more

The asteroid belt is also termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta, Pallas, and Hygiea. read more