Temporal data representing chronological observations of complex systems can be ubiquitously collected in smart industry, medicine, finance and etc. In the last decade, many tasks have been studied for mining temporal data and offered significant value for various applications. Among these tasks, causal discovery aims to understand the underlying generation mechanism of temporal data and has attracted much research attention. According to whether the data is calibrated, existing causal discovery approaches can be divided into two subtasks, i.e., multivariate time-series causal discovery, and event sequence causal discovery. Previous tutorials or surveys have primarily focused on causal discovery from time-series data and disregarded the second ones. In this tutorial, we elucidate the correlation between the two subtasks and provide a comprehensive review of the existing solutions. Moreover, we offer some potential applications and summarize new perspectives for discovering causal relations from temporal data. We hope the audiences can obtain a systematic overview of this topic and inspire some new ideas for their own research.