In the first part of the talk I will discuss doubling constructions. In particular I will discuss in some detail a recent doubling construction for an equatorial two-sphere in the round three-sphere, and also potential generalizations for self-shrinkers of the Mean Curvature flow. In the second part of the talk I will briefly discuss the current understanding of desingularization constructions for minimal surfaces and self-shrinkers. In the third and final part I will discuss open uniqueness questions for closed embedded minimal surfaces in the round three-sphere inspired by the above constructions.