The evolutionary search of a finite population in a rugged fitness or energy landscape with many local optima is a paradigmatic problem that connects evolutionary biology to the statistical physics of disordered systems and computer science. The talk will begin by introducing the basic concepts of fitness landscapes and evolutionary dynamics of Wright-Fisher type. I then describe a detailed numerical investigation of evolutionary trajectories in a sequence space of finite extent, which leads to a classification of dynamical regimes that are traversed with increasing population size [1]. Two analytically tractable limits - the limit of infinite population size [2] and the limit of infinite sequence length [3] - will be discussed in some detail, with particular emphasis on the relation to the theory of records. Finally, some preliminary results on the structure of empirical fitness landscapes determined in evolution experiments will be reported [4]. \\ \par \noindent [1] K. Jain, J. Krug, Genetics 175, 1275 (2007). \par \noindent [2] K. Jain, J. Krug, JSTAT (2005) P04008. \par \noindent [3] S.C. Park, J. Krug, JSTAT (2008) P04014. \par \noindent [4] J.A.G.M. de Visser, S.C. Park, J. Krug, arXiv:0807.3002.