The problem with those things is that their habitats and feeding places are very unsterile, which if you are bitten/stung can lead very quickly to a huge secondary infection. Take medical advice quickly if necessary.
The one I saw was the biggest horse fly I've ever seen.
I watched it for a while (mustn't have been a female on point of lay because it didn't show any interest in me or the horses in the adjacent fields) . Just sat there rubbing its fore legs together .