For the issue of translations between programming languages with observational semantics, this paper clarifies the notions, the relevant questions, and the methods, constructs a general framework, and provides several tools for proving various correctness properties of translations like adequacy and full abstractness, with a special emphasis on observational correctness. We will demonstrate that a wide range of programming languages and programming calculi and their translations can make advantageous use of our framework for focusing the analysis of their correctness.