This volume is about tree-like structures, namely semilinear ordering, general betweenness relations, $C$-relations and $D$-relations. It contains a systematic study of betweenness and introduces $C$ and $D$-relations to describe the behavior of points at infinity ('leaves' or 'ends' or 'directions') of trees. The focus is on structure theorems and on automorphism groups, with applications to the theory of infinite permutation groups. This work: offers the first systematic treatment of betweenness relations; introduces important new concepts of $C$-relations and $D$-relations; elucidates the close relationships between semilinear orderings, betweenness relations, $C$ and $D$-relations; and, considers their automorphism groups as important examples of Jordan permutation groups.