In recent work with Guy David we introduce the notion of almost
minimizer for a series of functionals previously studied by Alt-Caffarelli
and Alt-Caffarelli-Friedman.

We prove regularity results for these almost minimizers and explore the
structure of the corresponding free boundary. A key ingredient in the study
of the 2-phase problem is the existence of almost monotone quantities. The
goal of this talk is to present these results in a self-contained manner,
emphasizing both the similarities and differences between minimizers and
almost minimizers.