This paper advocates approaching timetable construction from the algorithms and complexity perspective, in which analysis of the specific problem under study is used to find efficient algorithms for some of its aspects, or to relate it to other problems. Examples are given of problem analyses leading to relaxations, phased approaches, very large-scale neighbourhood searches, bipartite matchings, ejection chains, and connections with standard NP-complete problems. Although a thorough treatment is not possible in a paper of this length, it is hoped that the examples will encourage timetabling researchers to explore further with a view to utilising some of the techniques in their own work.