This paper offers insights on the major issues and challenges firms face in the Covid-19 pandemic and their concerns for Corporate Social Responsibility (CSR) themes. To do so, we investigate large Italian firms' discussions on Twitter in the first nine months of the pandemic. Specifically, we ask: How is firms' Twitter discussion developing during the Covid-19 pandemic? Which CSR dimensions and topics do firms discuss? To what extent do they resonate with the public? We downloaded Twitter posts by the accounts of large Italian firms, and we built the bipartite network of accounts and hashtags. Using an entropy-based null model as a benchmark, we projected the information contained in the network into the accounts layers, identifying a network of accounts. We find that the network is composed of 13 communities and accounts at the core of the network focus on environmental sustainability, digital innovation, and safety. Firms' ownership type does not seem to influence the conversation. While the relevance of CSR hashtags and stakeholder engagement is relatively small, peculiarities arise in some communities. Overall, our paper highlights the contribution of online social networks and complex networks methods for management and strategy research, showing the role of online social media in understanding firms' issues, challenges, and responsibilities, with common narratives naturally emerging from data.