In the talk we consider inequalities of Hardy type for functions in Triebel-Lizorkin spaces. In particular, we discuss these inequalities for functions defined on domains whose boundary has the small Aikawa dimension  (the case of a 'thin' boundary). We also show the validity of Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary (the case of a 'fat' set). In addition, we would like to give a short exposition of various fatness conditions related to the theory, and apply Hardy inequalities in connection to the boundedness of extension operators for Triebel-Lizorkin spaces.