In causal discovery, the aim is to uncover the underlying causal mechanisms that drive the relationships between a collection of observed variables. It is a research topic with applications in many areas, including medicine, biology, economics, and social sciences. In principle, identifying causal relationships requires interventions (a.k.a., experiments). However, this 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 surveying the causal discovery field, I will discuss some recent advances, namely on causal discovery from data with latent interventions and on the quintessential causal discovery problem: distinguishing cause from effect on a pair of dependent variables.