Since its introduction in the social sciences in the 1980s, sequence analysis (SA) has enhanced our understanding of a broad range of social processes. In this chapter we recall fundamental underlying sociological concepts, such as narratives, trajectories, stages, events, transitions and the role of the context. We also differentiate levels of sequential complexity that have consequences on the way SA is applied. Following this, we sketch out the intellectual, technical and sociological factors that made SA converge around a core program defined by specific fieldwork, data, time frames and statistical tools. The core program has ensured a set of common standards, while at the same time leaving room for variants and alternatives. The book discusses both these standards and identifies a set of new challenges. Among these, sequence comparison implies rethinking about the notion of sequence, its sociological underpinnings, its mathematical robustness and the value of competing algorithms. Life course sequences continue innovating, for example on multiple life domains, linked lives, the subjective dimension of trajectories and the role of age. Beyond sociology, SA sheds new light on political issues at the levels of individuals, groups and institutions. Improvements also take place regarding sequence visualisation, from network graphs to event-based synchronisation and optimisation of graphical representation that are both rich in information and intuitive to capture.