How to remove duplicate elements

list = {1, 2, 1, 2, 3, 4, 5, 1};

Keys@Select[Counts[list], # == 1 &]
(* {3, 4, 5} *)

With[{t = Tally[#]}, Pick[t[[All, 1]], t[[All, 2]], 1]] &

Should outperform, hardly "ingenious "...

Without pattern matching:

Sort[{1, 2, 1, 2, 3, 4, 5, 1}] // 
  Split // 
  Select[Length[#] == 1 &] //
  Flatten[#, 1] &

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