The demand for systems that continue on operation by adapting themselves in response to disturbing changes in their environment has increased in the last decades. Those systems, termed self-adaptive software (SAS) systems, should be developed with techniques and methods appropriated for analysing and designing this kind of systems, starting from the requirements phase. Several contributions propose approaches to improve the specification of requirements for those systems. This paper aims to review the most significant challenges still open in the domains of languages for requirements specification and methods for model verification of self-adaptive systems, independently of their particular application areas. More concretely, the main contribution of this paper is a list of ten challenges to achieve a better-defined specification of requirements for SAS systems, and a more effective verification of such specifications. These challenges are well worthy of being addressed in both communities, the requirements engineering (RE) and the SAS one.