<p>The aim of this paper is to develop a unified theory of horizon and recession asymptotic notions for sets, functions, and multifunctions. This unified approach allows to exploit both the algebraic and topological features of these objects. We study the notion of regular set defined as a set for which its horizon and recession cones coincide. This notion plays an important role in the theory. Regular functions and multifunctions are defined and studied as well. By using the unified approach, we obtain properties, formulas, calculus rules, and relationships for horizon and recession notions. Finally, we study the horizon and recession mappings of various important functions and multifunctions from variational analysis.</p>