The study of denotations is usually kept separate from the study of beliefs. Truth and entailment belong to the former, probability and reasoning under uncertainty to the latter. Truth serves as the link between beliefs and the facts: The probability of (1a) is the probability that (1a) is true, which in turn is the probability that the match will light. (1) a. The match will light. b. If you strike the match, it will light. Things are more complicated when it comes to conditionals like (1b). Intuititions as well as empirical facts about the validity of inference patterns suggest that (T) should hold: (T) The probability of "if A then C" is the conditional probability of C, given A. But this leaves many questions unanswered. Lewis (1976) showed that a conditional probability cannot be interpreted as the probability that a proposition is true. Does it follow that conditionals do not have objective truth values? Empirically, too, (T) is problematic: It is not clear whether and how it applies to counterfactuals, and there are counterexamples with indicative conditionals as well. In this talk I will first briefly present some of the theoretical background of this work, including facts about inference patterns, the basic assumptions behind probabilistic inference (Adams, 1965, 1975, 1998), and the framework in which probabilities are encoded. I will then discuss in some detail one approach which, when implemented properly, addresses many of the open problems. The approach extends a proposal by Jeffrey (1991; cf. also Stalnaker and Jeffrey, 1994) to assign "truth values" to conditionals that are allowed to fall between 0 (False) and 1 (True) at worlds at which the antecedent is false. It is known that this avoids the problem Lewis pointed out, but beyond that it is mostly of technical interest and makes false predictions about the probabilities of some conditionals. The topic I will mostly focus on concerns the relationship between predictive conditionals like (2a) and their counterfactual counterparts (2b). (2) a. If you strike the match, it will light. b. If you had struck the match, it would have lit. It has often been suggested that the probability of (2b) is the probability (2a) had at an earlier time. But this cannot be generally right. For instance, the probability of (3b) depends on the outcome of the coin toss, whereas that of (3a) does not. (3) a. If you bet on heads, you will lose. b. If you had bet on heads, you would have lost. Based on examples like these, I will explore the possibility of interpreting Jeffrey's intermediate values of indicative conditionals as the values of the corresponding counterfactuals. It turns out that a simple unified account of these classes is provided by taking (qualitative) information about causal independence into account, much as in the "causal networks" recently used in Artificial Intelligence (Pearl, 2000). Finally, I will discuss another consequence of this approach: It predicts that the probabilities of conditionals are not always the corresponding conditional probabilities. In particular, the two come apart whenever the conditional is causally but not stochastically independent of its antecedent. I will argue that this is a feature, not a bug, for it accounts for a number of counterexamples found in the literature. I will conclude with some remarks on the generality of this approach and its computational relevance in Knowledge Representation.