Multiobjective optimization problems have attracted increasing interest in recent years due to many applications in various areas of modern human activity. Over the years, several solution concepts of vector optimization problems have been introduced into optimization theory and used in various applications for which multiobjective programming problems are models of real-world extremum problems. In this work, we concentrate on the presentation of various concepts of optimal solutions in some classes of vector optimization problems. Some relationships between them are also investigated. In order to clarify the theoretical results, some illustrative examples are also given.