  Causality lays the foundation for the trajectory of our world. Causal
inference (CI), which aims to infer intrinsic causal relations among variables
of interest, has emerged as a crucial research topic. Nevertheless, the lack of
observation of important variables (e.g., confounders, mediators, exogenous
variables, etc.) severely compromises the reliability of CI methods. The issue
may arise from the inherent difficulty in measuring the variables.
Additionally, in observational studies where variables are passively recorded,
certain covariates might be inadvertently omitted by the experimenter.
Depending on the type of unobserved variables and the specific CI task, various
consequences can be incurred if these latent variables are carelessly handled,
such as biased estimation of causal effects, incomplete understanding of causal
mechanisms, lack of individual-level causal consideration, etc. In this survey,
we provide a comprehensive review of recent developments in CI with latent
variables. We start by discussing traditional CI techniques when variables of
interest are assumed to be fully observed. Afterward, under the taxonomy of
circumvention and inference-based methods, we provide an in-depth discussion of
various CI strategies to handle latent variables, covering the tasks of causal
effect estimation, mediation analysis, counterfactual reasoning, and causal
discovery. Furthermore, we generalize the discussion to graph data where
interference among units may exist. Finally, we offer fresh aspects for further
advancement of CI with latent variables, especially new opportunities in the
era of large language models (LLMs).
