The optimal solution set is the set of all optimal solutions over all realizations of interval entries. Determining this set is a basic yet very challenging problem. Many open questions remain in this area; for example, no simple (closed-form) characterization of the set is known. That is why we also focus on approximation, proposing several inner and outer estimation techniques. Further, we present an algorithm to check whether a given point belongs to the optimal set; due to the NP-hardness of the problem, the method can be exponential for certain LP forms. The last issue discussed is the boundedness of the optimal set of each LP realization (not to be confused with boundedness of the overall optimal set).