  In this topical review we argue that neutrino mass and mixing data motivates
extending the Standard Model to include a non-Abelian discrete flavour symmetry
in order to accurately predict the large leptonic mixing angles and CP
violation. We begin with an overview of the Standard Model puzzles, followed by
a description of some classic lepton mixing patterns. Lepton mixing may be
regarded as a deviation from tri-bimaximal mixing, with charged lepton
corrections leading to solar mixing sum rules, or tri-maximal lepton mixing
leading to atmospheric mixing rules. We survey neutrino mass models, using a
roadmap based on the open questions in neutrino physics. We then focus on the
seesaw mechanism with right-handed neutrinos, where sequential dominance (SD)
can account for large lepton mixing angles and CP violation, with precise
predictions emerging from constrained SD (CSD). We define the flavour problem
and discuss progress towards a theory of flavour using GUTs and discrete family
symmetry. We classify models as direct, semidirect or indirect, according to
the relation between the Klein symmetry of the mass matrices and the discrete
family symmetry, in all cases focussing on spontaneous CP violation. Finally we
give two examples of realistic and highly predictive indirect models with CSD,
namely an A to Z of flavour with Pati-Salam and a fairly complete $A_4\times
SU(5)$ SUSY GUT of flavour, where both models have interesting implications for
leptogenesis.
