Crises such as the COVID-19 pandemic continuously threaten our world and emotionally affect billions of people worldwide in distinct ways. Understanding the triggers leading to people's emotions is of crucial importance. Social media posts can be a good source of such analysis, yet these texts tend to be charged with multiple emotions, with triggers scattering across multiple sentences. This paper takes a novel angle, namely, emotion detection and trigger summarization, aiming to both detect perceived emotions in text, and summarize events that trigger each emotion. To support this goal, we introduce CovidET (Emotions and their Triggers during Covid-19), a dataset of ~1,900 English Reddit posts related to COVID-19, which contains manual annotations of perceived emotions and abstractive summaries of their triggers described in the post. We develop strong baselines to jointly detect emotions and summarize emotion triggers. Our analyses show that CovidET presents new challenges in emotion-specific summarization, as well as multi-emotion detection in long social media posts.