This paper is a survey of the recent advances in several directions in the class of \(p\)-sequential spaces and \(p\)-Fréchet-Urysohn spaces, which generalize the sequential spaces and the Fréchet-Urysohn spaces by replacing the Fréchet filter on \(\omega\) by an arbitrary filter (mostly a free ultrafilter) \(p\) on \(\omega\). The sections are: general topological spaces, \(p\)-compact spaces, compact spaces, topological groups and sequentiality and \(p\)-sequentiality in topological function spaces. More than 30 problems are raised.