  We survey the state of the art on amalgamation in varieties of semilinear
residuated lattices. Our discussion emphasizes two prominent cases from which
much insight into the general picture may be gleaned: idempotent varieties and
their generalizations ($n$-potent varieties, knotted varieties), and
cancellative varieties and their relatives (MV-algebras, BL-algebras). Along
the way, we illustrate how general-purpose tools developed to study
amalgamation can be brought to bear in these contexts and solve some of the
remaining open questions concerning amalgamation in semilinear varieties. Among
other things, we show that the variety of commutative semilinear residuated
lattices does not have the amalgamation property. Taken as a whole, we see that
amalgamation is well understood in most interesting varieties of semilinear
residuated lattices, with the last few outstanding open questions remaining
principally in the cancellative setting.
