Abstract: The FAIR Guiding Principles, published in 2016, aim to improve the findability, accessibility, interoperability and reusability of digital research objects for both humans and machines. Until now the FAIR principles have been mostly applied to research data. The ideas behind these principles are, however, also directly relevant to research software. Hence there is a distinct need to explore how the FAIR principles can be applied to software. In this work, we aim to summarize the current status of the debate around FAIR and software, as a basis for the development of definite community-agreed principles for FAIR research software in the future. We discuss what makes software different from data with respect to the application of the FAIR principles, present an analysis of where the existing principles can directly be applied to software, where they need to be adapted or reinterpreted, and where the definition of additional principles is required. Furthermore, we discuss desired characteristics of research software that go beyond FAIR.