The impact of the Covid‐19 pandemic and ensuing social restrictions has been profound, affecting the health, livelihoods, and wellbeing of populations worldwide. Studies have shown widespread effects on mental health, with an increase in stress, loneliness, and depression symptoms related to the pandemic. Media plays a critical role in containing and managing crises, by informing society and fostering positive behavior change. Social restrictions have led to a large increase in reliance on online media channels, and this can influence mental health and wellbeing. Anxiety levels, for instance, may be exacerbated by exposure to Covid‐related content, contagion of negative sentiment among social networks, and “fake news.” In some cases, this may trigger abstinence, leading to isolation and limited access to vital information. To be able to communicate distressing news during crises while protecting the wellbeing of individuals is not trivial; it requires a deeper understanding of people's emotional response to online and social media content. This paper selectively reviews research into consequences of social media usage and online news consumption for wellbeing and mental health, focusing on and discussing their effects in the context of the pandemic. Advances in Artificial Intelligence and Data Science, for example, Natural Language Processing, Sentiment Analysis, and Emotion Recognition, are discussed as useful methods for investigating effects on population mental health as the pandemic situation evolves. We present suggestions for future research, and for using these advances to assess large data sets of users' online content, to potentially inform strategies that enhance the mental health of social media users going forward.