The emergence or re-emergence of viruses with epidemic and/or pandemic potential, such as Ebola, Zika, Middle East Respiratory Syndrome (MERS-CoV), Severe Acute Respiratory Syndrome Coronavirus 1 and 2 (SARS and SARS-CoV-2) viruses, or new strains of influenza represents significant human health threats due to the absence of available treatments. Vaccines represent a key answer to control these viruses. However, in the case of a public health emergency, vaccine development, safety, and partial efficacy concerns may hinder their prompt deployment. Thus, developing broad-spectrum antiviral molecules for a fast response is essential to face an outbreak crisis as well as for bioweapon countermeasures. So far, broad-spectrum antivirals include two main categories: the family of drugs targeting the host-cell machinery essential for virus infection and replication, and the family of drugs directly targeting viruses. Among the molecules directly targeting viruses, nucleoside analogues form an essential class of broad-spectrum antiviral drugs. In this review, we will discuss the interest for broad-spectrum antiviral strategies and their limitations, with an emphasis on virus-targeted, broad-spectrum, antiviral nucleoside analogues and their mechanisms of action.