A number is said to be y-friable (or y-smooth) if all of
its prime factors
are at most y. An important problem is to establish the distribution of
y-friable numbers less than x in arithmetic progressions to modulus q,
on as wide a range of x, y, and q as possible. I will discuss an approach
of Soundararajan to this problem, and then discuss some of my work
that extends the ranges of x and y in Soundararajan's result.