The human respiratory syncytial virus (RSV) is a negative-sense, single-stranded RNA virus. It is the major cause of severe acute lower respiratory tract infection in infants, the elderly population, and immunocompromised individuals. There is still no approved vaccine or antiviral treatment against RSV disease, but new monoclonal prophylactic antibodies are yet to be commercialized, and clinical trials are in progress. Hence, urgent efforts are needed to develop efficient therapeutic treatments. RSV RNA synthesis comprises viral transcription and replication that are catalyzed by the large protein (L) in coordination with the phosphoprotein polymerase cofactor (P), the nucleoprotein (N), and the M2-1 transcription factor. The replication/transcription is orchestrated by the L protein, which contains three conserved enzymatic domains: the RNA-dependent RNA polymerase (RdRp), the polyribonucleotidyl transferase (PRNTase or capping), and the methyltransferase (MTase) domain. These activities are essential for the RSV replicative cycle and are thus considered as attractive targets for the development of therapeutic agents. In this review, we summarize recent findings about RSV L domains structure that highlight how the enzymatic activities of RSV L domains are interconnected, discuss the most relevant and recent antivirals developments that target the replication/transcription complex, and conclude with a perspective on identified knowledge gaps that enable new research directions.