A minimal surface is doubly periodic if it is invariant under two linearly independent translations (but not three). To be embedded, it needs to have annular ends (also called Scherk ends) that are asymptotic to half planes.

- Non-parallel annular top and bottom ends
- Parallel top and bottom ends
- Genus 1
- Genus 2
- Genus 3
- Higher Genus
- Higher Genus Wei Surfaces
- Other higher genus examples

- Exotic ends