The thesis explores causal inference with a specific focus on the Probability of Causation (PC), which is the probability that a treatment was the cause of an observed outcome. It analyzes the determination of bounds on PC in scenarios where the variables involved (treatment, outcome, mediators, or covariates) are binary, discrete, or continuous. The conditions under which these bounds become tighter or looser are examined, depending on the assumed causal structure and the nature of the variables. The work offers a systematization of theoretical results and assesses their applicability to practical cases, with particular reference to causal responsibility in clinical or legal contexts.