  Understanding causality helps to structure interventions to achieve specific
goals and enables predictions under interventions. With the growing importance
of learning causal relationships, causal discovery tasks have transitioned from
using traditional methods to infer potential causal structures from
observational data to the field of pattern recognition involved in deep
learning. The rapid accumulation of massive data promotes the emergence of
causal search methods with brilliant scalability. Existing summaries of causal
discovery methods mainly focus on traditional methods based on constraints,
scores and FCMs, there is a lack of perfect sorting and elaboration for deep
learning-based methods, also lacking some considers and exploration of causal
discovery methods from the perspective of variable paradigms. Therefore, we
divide the possible causal discovery tasks into three types according to the
variable paradigm and give the definitions of the three tasks respectively,
define and instantiate the relevant datasets for each task and the final causal
model constructed at the same time, then reviews the main existing causal
discovery methods for different tasks. Finally, we propose some roadmaps from
different perspectives for the current research gaps in the field of causal
discovery and point out future research directions.
