This chapter reviews the various flow routing algorithms that simulate the distribution and flow of water across landscapes. The distinguishing characteristics of nine such algorithms and the experiments that have been conducted to evaluate their performance over the past 15 years are discussed. From there, we consider three sets of enduring challenges: (1) the role of scale and feedback between soil and water, and the need to consider these issues when characterizing the properties of both; (2) the need for dynamic flow routing algorithms and related indices in many landscapes; and (3) some of the as yet unrealized opportunities for treating space and time as continuous variables in the representation of soil water properties. The chapter concludes by noting the current state-of-the-art and where we might go from here.