This master’s thesis deals with a special class of random walks on \(\mathbb{Z}\) in random and nonrandom media called multi-excited random walks on integers, more popularly known as cookie random walks. In this walk a nearest neighbor random walk on \(\mathbb{Z}\) is launched in such a way that at each site the random walker has a drift to the right, the strength of which depends on the environment at that site and how many times the walker has visited the site before. The main goal of the thesis is to give necessary and sufficient conditions for recurrence of the walk, to give expression for the speed of the walk, and to apply those results to the walk described in Example 0.1. In Chapter 1 the basic notations are introduced and the properties of the walk in fixed environment are analyzed. This chapter is a preparation for the main results in random environments. The second chapter deals with walks in random environments, i.e. the probability of moving to the right also has some distribution. It is assumed that the environments are stationary and ergodic. Theorem 2.14 contains the proof of the main result of the thesis, a criterion for recurrence and transience, and this result is applied to some specific random walks. The next topic of this thesis is the existence of speed of random walks, which is defined as a limit of the ratio of the displacement from the starting position and current running time of a walk, i.e. \(\lim\limits_{n\to\infty}\frac{X_n}{n}\) if we start from 0. It is proven that such speed exists almost surely for every walk (Theorem 2.21). The last part of the thesis returns to the walk from Example 0.1. The exact formula for the probability that the walker will never return to 0 (Theorem 2.29) is computed and it is proven that the walk in Example 0.1 has zero speed when \(p<1\), even when the walk is transient (Theorem 2.31).