  Categorical orthodoxy has it that collections of ordinary mathematical
structures such as groups, rings, or spaces, form categories (such as the
category of groups); collections of 1-dimensional categorical structures, such
as categories, monoidal categories, or categories with finite limits, form
2-categories; and collections of 2-dimensional categorical structures, such as
2-categories or bicategories, form 3-categories.
  We describe a useful way in which to regard bicategories as objects of a
2-category. This is a bit surprising both for technical and for conceptual
reasons. The 2-cells of this 2-category are the crucial new ingredient; they
are the icons of the title. These can be thought of as ``the oplax natural
transformations whose components are identities'', but we shall also give a
more elementary description.
  We describe some properties of these icons, and give applications to monoidal
categories, to 2-nerves of bicategories, to 2-dimensional Lawvere theories, and
to bundles of bicategories.
