Knowing the value of biodiversity would enable more efficient preservation choices. For this purpose it is useful to have quantitative and/or qualitative information on the object “biodiversity”. We sum up here several literatures (ecology, biology, political sciences and economics) which attempt to define and measure biodiversity. The originality of this note is that it clarifies the axiomatic bases of the indicators. While theoretical bases are sometimes fragile and need to be confirmed, practical issues are also a challenge for research.