This paper includes a concise survey of the work done in order to extend de Finetti's coherence condition to the prevision of conditional random quantities. Sections 1 and 2 deal with the equivalence among different formulations of the extended condition and analyse the relations between it and the usual axiomatic treatment of finitely additive probabilities and previsions. Sections 3 and 4 include some results and remarks about the extensibility of a coherent conditional prevision. Finally, Sections 5 and 6 consider conglomerative previsions in order to frame Kolmogorov's theory of conditional probability and expectation into the more general approach sketched in the previous sections.