  Emergence and causality are two fundamental concepts for understanding
complex systems. They are interconnected. On one hand, emergence refers to the
phenomenon where macroscopic properties cannot be solely attributed to the
cause of individual properties. On the other hand, causality can exhibit
emergence, meaning that new causal laws may arise as we increase the level of
abstraction. Causal emergence theory aims to bridge these two concepts and even
employs measures of causality to quantify emergence. This paper provides a
comprehensive review of recent advancements in quantitative theories and
applications of causal emergence. Two key problems are addressed: quantifying
causal emergence and identifying it in data. Addressing the latter requires the
use of machine learning techniques, thus establishing a connection between
causal emergence and artificial intelligence. We highlighted that the
architectures used for identifying causal emergence are shared by causal
representation learning, causal model abstraction, and world model-based
reinforcement learning. Consequently, progress in any of these areas can
benefit the others. Potential applications and future perspectives are also
discussed in the final section of the review.
