The present paper discusses some recent and current challenges for the banking system in the European Union (EU). While Section 1 develops on its overall robustness before the onset of the pandemic crisis and briefly overviews the regulatory and supervisory responses to preserve its stability amidst that crisis, Section 2 focuses on two challenges relating to potential threats to banking stability in the EU: non-performing loans and negative central bank interest rates. Section 3 addresses then the challenges linked to EU regulatory developments in the fields of sustainable and digital finance. Finally, Section 4 contains a final assessment and the concluding remarks.