This chapter presents various advanced aspects of random walks. The first concerns self-avoiding random walks, which were originally proposed as models for unbranched polymers. These random walks are characterized by the restriction that each point may only be visited once. If the position of a random walk after nnn steps is the sum of nnn independent and identically distributed random vectors, the distribution of the individual summands can, in principle, be arbitrary. Relevant references in the literature are provided on this topic. Another topic explores random walks on the vertices of a graph. For finite graphs, one point of interest is the so-called cover time, which is the expected number of steps required to visit every vertex starting from a given one. The chapter concludes with a connection between random walks and electrical networks.