Since the beginning of MCMC sampling and the introduction of the Metropolis algorithm, constant efforts have been made on developing fast Markov chains which do not present any diffusive behavior while sampling the correct distribution. However, almost all of the developed schemes are reversible, obey detailed balance and rely on rejections to achieve the correct invariant distribution. During a talk presented at MATRIX, I explained how the exploitation of system symmetries allows to break detailed balance, while satisfying the necessary condition of the global one. This leads to the design of continuous-time and non-reversible Markov processes, which, being rejection-free, display interesting dynamical properties. First known as Event-Chain Monte Carlo algorithms, these processes can actually be characterized as Piecewise Deterministic Markov Processes. I then explored how this robust characterization enables us to delve deeper into distinguishing between what is necessary and what is merely sufficient to achieve effective exploitation, and how it can be leveraged in algorithmic design.