  An additive submonoid of the nonnegative cone of the real line is called a
positive monoid. Positive monoids consisting of rational numbers (also known as
Puiseux monoids) have been the subject of several recent papers. Moreover,
those generated by a geometric sequence have also received a great deal of
recent attention. Our purpose is to survey many of the recent advances
regarding positive monoids, and we provide numerous examples to illustrate the
complexity of their atomic and arithmetic structures.
