DLEK and DSEK
With advancement in techniques and knowledge, there are certain conditions where only a specific portion of the cornea is affected.  Therefore, only those affected portions are replaced.  Around the year 2000, some corneal surgeons started with performing Deep Lamellar Endothelial Keratoplasty (DLEK), which replaced a portion of the inside cornea, and placed a new inlay in place.  Below is Visante image of a patient of Dr. Ash that had DLEK Surgery.  See how a portion was removed and then replaced.



Unfortunately, DLEK did not result in universally accepted vision.  DLEK was then transitioned to Descemet Stripping Endothelial Keratoplasty around 2004.  In this procedure, a very thin layer of the inner lining of the cornea is removed (not visible in the Visante image below) and simply an inlay of inner cornea is inserted in the eye and attached to the native cornea.  See below, a DSEK image of Dr. Ash patient, this inlay is more like an addition to the cornea.

The Above cornea best exemplifies the anatomic changes with DSEK first day after surgery.  Once the Cornea is much more healed and the swelling is resolved, the below image 6 week later shows the progress.