  In this paper we study the theory of {\it pseudo knots}, which are knots with
some missing crossing information, and we introduce and study the theory of
{\it pseudo tied links} and the theory of {\it pseudo knotoids}. In particular,
we first present a braiding algorithm for pseudo knots and we then introduce
the $L$-moves in that setting, with the use of which we formulate a sharpened
version of the analogue of the Markov theorem for pseudo braids. Then we
introduce and study the theory of {\it tied pseudo links}, that generalize the
notion of tied links, and we exploit the relation between tied pseudo links and
tied singular links. We first present an $L$-move braid equivalence for tied
singular braids. Then, we introduce the tied pseudo braid monoid and we
formulate and prove analogues of the Alexander and Markov theorems for tied
pseudo links. Finally, we introduce and study the theory of {\it pseudo
knotoids}, that generalize the notion of knotoids. We present an isotopy
theorem for pseudo knotoids and we then pass to the level of braidoids. We
further introduce and study the {\it pseudo braidoids} by introducing the {\it
pseudo} $L${\it -moves} and by presenting the analogues of the Alexander and
Markov theorems for pseudo knotoids. We also discuss further research related
to {\it tied (multi)-knotoids and tied pseudo (multi)-knotoids}. The theory of
pseudo knots may serve as a strong tool in the study of DNA, while tied links
have potential use in other aspects of molecular biology.
