  We review the physical motivations and the mathematical results obtained so
far in the isocone-based approach to noncommutative causality. We also give a
briefer account of the alternative framework of Franco and Eckstein which is
based on Lorentzian spectral triples. We compare the two theories on the simple
example of the product geometry of the Minkowski plane by the finite
noncommutative space with algebra $M_2({\mathbb C})$.
