The 2005 AISC LRFD Specifications for Structural Steel Buildings are making it possible for designers to recognize explicitly the structural resistance provided within the elastic and inelastic ranges of behavior and up to the maximum load limit state. There is an increasing awareness of the need for practical second-order analysis approaches for a direct determination of overall structural system response. This paper attempts to present a simple, concise and reasonably comprehensive introduction to some of the theoretical and practical approaches which have been used in the traditional and modern processes of design of steel building structures.