  Asteroids and meteorites provide key evidence on the formation of
planetesimals in the Solar System. Asteroids are traditionally thought to form
in a bottom-up process by coagulation within a population of initially km-scale
planetesimals. However, new models challenge this idea by demonstrating that
asteroids of sizes from 100 to 1000 km can form directly from the gravitational
collapse of small particles which have organised themselves in dense filaments
and clusters in the turbulent gas. Particles concentrate passively between
eddies down to the smallest scales of the turbulent gas flow and inside
large-scale pressure bumps and vortices. The streaming instability causes
particles to take an active role in the concentration, by piling up in dense
filaments whose friction on the gas reduces the radial drift compared to that
of isolated particles. In this chapter we review new paradigms for asteroid
formation and compare critically against the observed properties of asteroids
as well as constraints from meteorites. Chondrules of typical sizes from 0.1 to
1 mm are ubiquitous in primitive meteorites and likely represent the primary
building blocks of asteroids. Chondrule-sized particles are nevertheless
tightly coupled to the gas via friction and are therefore hard to concentrate
in large amounts in the turbulent gas. We review recent progress on
understanding the incorporation of chondrules into the asteroids, including
layered accretion models where chondrules are accreted onto asteroids over
millions of years. We highlight in the end ten unsolved questions in asteroid
formation where we expect that progress will be made over the next decade.
