  Many infinite-dimensional Lie groups of interest can be expressed as a union
of an ascending sequence of (finite- or infinite-dimensional) Lie groups. In
this survey article, we compile general results concerning such ascending
unions, describe the main classes of examples, and explain what the general
theory tells us about these.
  In particular, we discuss:
  (1) Direct limit properties of ascending unions of Lie groups in the relevant
categories;
  (2) Regularity in Milnor's sense;
  (3) Homotopy groups of direct limit groups and of Lie groups containing a
dense union of Lie groups;
  (4) Subgroups of direct limit groups;
  (5) Constructions of Lie group structures on ascending unions of Lie groups.
