  In this paper, we are interested in parallels to the classical notions of
special subsets in $\R$ defined in the generalized Cantor and Baire spaces
($2^\kappa$ and $\kappa^\kappa$). We consider generalizations of the well-known
classes of special subsets, like Lusin sets, strongly null sets, concentrated
sets, perfectly meagre sets, $\sigma$-sets, $\gamma$-sets, sets with Menger,
Rothberger or Hurewicz property, but also of some less-know classes like
$X$-small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver,
Miller and Laver-null sets. We notice that many classical theorems regarding
these classes can be relatively easy generalized to higher cardinals although
sometimes with some additional assumptions. This paper serves as a catalogue of
such results along with some other generalizations and open problems.
