Our work deals with model theory of ordered structures in the domain of end ex­tension problems. We prove four new theorems in this dissertation. Theorem I generalizes a classical theorem of Keisler and Morley and positively answers a question of Enayat. Theorems II and III deal with recursively saturated models, and is inspired by the works of Shelah and Schmerl (respectively). Finally, theorem IV fine­tunes a fundamental result of Keisler on singular­like models.

• Theorem I. Every countable model of ZFC has elementary end exten­sions with arbitrary cofinality.

• Theorem II. Suppose κ is an inaccessible cardinal and T is a first­order theory with a κ­like model. Let A be a countable recursively saturated model of T . Then A has an elementary end extension with arbitrary cardinality and cofinality.

• Theorem III. Suppose κ is an inaccessible cardinal and T is a first­order theory with a κ­like model that embeds a stationary subset of κ. Let A be a countable recursively saturated model of T . Then A has a blunt minimal elementary end extension.

• Theorem IV. Suppose κ is an inaccessible cardinal and T is a first­order theory with a κ­like model. Let λ be a singular cardinal, then Keisler λ­like models of T can be represented as the union of a nice elementary end extension chain.