Causal discovery is an active research field that aims to uncover the underlying causal mechanisms that drive the relationship between a collection of variables and which has applications in many areas, including medicine, biology, economics, and social sciences. In principle, identifying causal relationships requires interventions. However, intervening is often impossible, impractical, or unethical, which has stimulated much research on causal discovery from purely observational data or mixed observational-interventional data. In this talk, after overviewing the causal discovery field, I will discuss some recent advances, namely on causal discovery from data with latent interventions and on what is the quintessential causal discovery problem: distinguishing the cause from the effect on a pair of dependent variables.