: You can set WhatsApp to automatically save all received videos. Go to Settings > Storage and Data > Media auto-download and ensure "Videos" is checked for Wi-Fi or Mobile Data. On WhatsApp Web or Desktop How To Download Video On Whatsapp Web
Depending on where you are viewing the video, the steps to save it to your local storage vary.
: Open the video in your chat. On Android, tap the three dots [⋮] and select Save . On iPhone, tap the Share icon and select Save Video .