It is known that YM2 with gauge group SU(N) is equivalent to a string theory with coupling gs=1/N, order by order in the 1/N expansion. We show how this result can be obtained from the bosonization of the fermionic formulation of YM2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM2 partition function of order exp{−kA/(πα′gs)} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead strictly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM2 is described by a perturbative string theory separated from a region where it is described by a topological string theory