We introduce BeDiscovER (Benchmark of Discourse Understanding in the Era of Reasoning Language Models), an up-to-date, comprehensive suite for evaluating the discourse-level knowledge of modern LLMs. BeDiscovER compiles 5 publicly available discourse tasks across discourse lexicon, (multi-)sentential, and documental levels, with in total 52 individual datasets. It covers both extensively studied tasks such as discourse parsing and temporal relation extraction, as well as some novel challenges such as discourse particle disambiguation (e.g., ``just''), and also aggregates a shared task on Discourse Relation Parsing and Treebanking for multilingual and multi-framework discourse relation classification. We evaluate open-source LLMs: Qwen3 series, DeepSeek-R1, and frontier model such as GPT-5-mini on BeDiscovER, and find that state-of-the-art models exhibit strong performance in arithmetic aspect of temporal reasoning, but they struggle with full document reasoning and some subtle semantic and discourse phenomena, such as rhetorical relation recognition.