  We identify the scaling limit of random intersection graphs inside their
critical windows. The limit graphs vary according to the clustering regimes,
and coincide with the continuum Erdos--Renyi graph in two out of the three
regimes. Our approach to the scaling limit relies upon the close connection of
random intersection graphs with binomial bipartite graphs, as well as a graph
exploration algorithm on the latter. This further allows us to prove limit
theorems for the number of triangles in the large connected components of the
graphs.
