The purpose of the study was to present the discussion between two accounts of conditional reasoning: the mental model theory and the suppositional account. The paper present a critical analysis of both accounts with the review of the arguments provided by the proponents of both theories. According to the mental model account conditional inference is made through building mental models compatible with the information given in the premises. The models can be modified by means of semantic and pragmatic modulation. The proponents of the suppositional theory state that basic understanding of a conditional is psychologically equivalent to the conditional probability of the consequent given the antecedent. The conflict between both accounts may be a result of different methodologies but the main argument concerns the assumption of the truth-functionality. In the view of the model theory the beliefs are certain if there are no counterexamples that contradict those beliefs.