In this thesis, we investigate attack vectors against Markov decision processes anddynamical systems. This work is motivated by the recent interest in the researchcommunity towards making Machine Learning models safer to malicious attacks. Wefocus on different attack vectors: (I) attacks that alter the input/output signal of aMarkov decision process; (II) eavesdropping attacks whose aim is to detect a change ina dynamical system; (III) poisoning attacks against data-driven control methods.(I) For attacks on Markov decision processes we focus on 2 types of attacks: (1) attacksthat alter the observations of the victim, and (2) attacks that alter the control signalof the victim. Regarding (1), we investigate the problem of devising optimal attacksthat minimize the collected reward of the victim. We show that when the policy andthe system are known to the attacker, designing optimal attacks amounts to solving aMarkov decision process. We also show that, for the victim, the system uncertaintiesinduced by the attack can be modeled using a Partially Observable Markov decisionprocess (POMDP) framework. We demonstrate that using Reinforcement Learningmethods tailored to POMDP lead to more resilient policies. Regarding (2), we insteadinvestigate the problem of designing optimal stealthy poisoning attacks on the controlchannel of Markov decision processes. Previous work constrained the amplitude ofthe adversarial perturbation, with the hope that this constraint will make the attackimperceptible. However, such constraints do not grant any level of undetectabilityand do not take into account the dynamic nature of the underlying Markov process.To design an optimal stealthy attack, we investigate a new attack formulation, basedon information-theoretical quantities, that considers the objective of minimizing thedetectability of the attack as well as the performance of the controlled process.(II) In the second part of this thesis we analyse the problem where an eavesdropper triesto detect a change in a Markov decision process. These processes may be affected bychanges that need to remain private. We study the problem using theoretical tools fromoptimal detection theory to motivate a definition of online privacy based on the averageamount of information per observation of the underlying stochastic system. We provideways to derive privacy upper-bounds and compute policies that attain a higher privacylevel, concluding with examples and numerical simulations.(III) Lastly, we investigate poisoning attacks against data-driven control methods.Specifically, we analyse how a malicious adversary can slightly poison the data soas to minimize the performance of a controller trained using this data. We show thatidentifying the most impactful attack boils down to solving a bi-level non-convexoptimization problem, and provide theoretical insights on the attack. We present ageneric algorithm finding a local optimum of this problem and illustrate our analysisfor various techniques. Numerical experiments reveal that minimal but well-craftedchanges in the data-set are sufficient to deteriorate the performance of data-drivencontrol methods significantly, and even make the closed-loop system unstable.