The diverse host range, high transmissibility, and rapid evolution of influenza A viruses justify the importance of containing pathogenic viruses studied in the laboratory. Other than physically or mechanically changing influenza A virus containment procedures, modifying the virus to only replicate for a single round of infection similarly ensures safety and consequently decreases the level of biosafety containment required to study highly pathogenic members in the virus family. This biological containment is more ideal because it is less apt to computer, machine, or human error. With many necessary proteins that can be deleted, generation of single-cycle infectious influenza A viruses (sciIAV) can be achieved using a variety of approaches. Here, we review the recent burst in sciIAV generation and summarize the applications and findings on this important human pathogen using biocontained viral mimics.