If you check the weather prediction on your phone, you might read that there is a 30 percent chance of rain at 4:00 in the afternoon. What does this mean? More precisely, what is the fraction 30/100 a measure of? Probability is a concept that is widespread both in everyday life and in science. Ordinary speakers of English utter and have some understanding of sentences such as “I will probably be late for the meeting,” or “it’s unlikely that Luxembourg will win the next World Cup.” Various sciences make explicit probabilistic claims: “the probability that a radium atom will decay in 1620 years is 0.5”; “the probability that a house mouse whose father is heterozygous for the t haplotype will inherit that trait is 0.9.” Other claims implicitly invoke probability: “the life expectancy of a child born in Japan today is 85.3 years.” Probability theory is also a major branch of mathematics, and it was given its modern formulation by Kolmogorov in 1933. Kolmogorov’s formalism presents a function P that satisfies a set of axioms: it is non-negative, normalized, and additive. These axioms entail a rich set of theorems concerning the behavior of P; together they make up the probability calculus. While the resulting theory is a formal theory in its own right, it is also natural to interpret P—to attach meanings, or truth conditions to claims involving it. ‘What is P?’, one may ask. This may be understood as a metaphysical question about what kinds of things are probabilities, or more generally as a question about what makes probability statements true or false. The various interpretations of probability attempt to answer this question, one way or another. This article surveys the literature on the interpretations of probability, due to mathematicians and especially philosophers. It divides the interpretations into two broad categories. Epistemological interpretations understand probability in terms of an agent’s beliefs, the strength of evidence in support of a statement, or other epistemological categories. Physical interpretations view probability as a feature of the world that would exist regardless of what evidence exists or what agents believe. This is a natural taxonomy, but others could be adopted, and its sub-categories are also somewhat pliable. The authors would like to thank Kim Border, Chris Bottomley, Kenny Easwaran, Hanti Lin, Charles Sebens, Glenn Shafer, Julia Staffel, Jeremy Strasser, and an anonymous referee for many helpful suggestions.