  In the first part of the paper we discuss the current status of the
application of the gluing methodology to doubling and desingularization
constructions for minimal surfaces in Riemannian three-manifolds. In particular
a doubling construction for equatorial spheres in $S^3(1)$ is announced.
Aspects of the current understanding of existence and uniqueness questions for
closed minimal embedded surfaces in $S^3(1)$ are also discussed, and some new
uniqueness questions are proposed. In the second part of the paper we discuss
some of the ideas and provide an outline for a general desingularization
construction without imposed symmetries.
  This paper is the author's contribution to the volume in honor of Professor
Richard M. Schoen's sixtieth birthday.
