In this paper, we give an overview of well-known routing and wavelength assignment (RWA) algorithms, and develop a novel classification for some of their main features. The objective of this paper is to show functional aspects of routing and wavelength assignement algorithms in WDM routing networks. Based on this classification, we compare different solutions for each category. Several challenges and trade-offs are identified. Although no algorithm in our study is a clear winner, advantages and disadvantages of several functional characteristics are discussed in order to help a system developer make a reasonable choice among candidate algorithms. In this study, we only consider algorithms for the off-line model (static traffic condition).