I will discuss some non-Markovian random walks as paradigms of stochastic processes with memory, In particular, in the first part I will discuss generic insights into large deviations and fluctuation mechanisms in systems with long-range memory [based mainly on joint work with Rob Jack]. In the second part, I will demonstrate how such a random walk framework can be used to model repeated decision-making with distorted human recall of past experiences. In the case of two choices with different utility distributions, it is possible for an agent to become "trapped" in the objectively worse choice on the basis of early experiences. Significantly, it turns out that, under certain conditions, there is a optimal level of noise in the decision process which maximizes the expected returns in the long run [based on joint work with Evangelos Mitsokapas].