  In this paper, we study toric ideals generated by circuits. For toric ideals
which have squarefree quadratic initial ideals, a sufficient condition to be
generated by circuits is given. In particular, squarefree Veronese subrings,
the second Veronese subrings and configurations arising from root systems
satisfy the condition. In addition, we study toric ideals of finite graphs and
characterize the graphs whose toric ideals are generated by circuits u -v such
that either u or v is squarefree. There exists several classes of graphs whose
toric ideals satisfy this condition and whose toric rings are nonnormal.
