Snapchat have updated Family Center again, this time adding controls that block 'sensitive' and 'suggestive' content from viewing by under 18's. To enable this feature, parents can toggle on the 'Restrict Sensitive Content' filter within Snapchat's Family Center and once enabled under 18's should not be able to see the blocked content, although this is only on Stories and Spotlight (short videos). It has no effect on content shared in Chat, Snaps and Search, so it is pretty limited.
More information for parents about this new feature can be found HERE and an explanation in regards to what Snapchat considers sensitive content can be found HERE.