The field of science communication is constantly evolving and searching for new ways and tools to improve its practice. Several studies have focused on how people are reached, the existing communication gaps and challenges and how communication can change people’s understanding, perception and use of science. However, a key element, namely, the public’s perception of this matter, has been mostly overlooked in the literature. This chapter presents the results of an in-depth qualitative analysis of the views of 500 European citizens on how to improve science communication. Their participation in the public consultations not only allowed for listening to their concerns and suggestions but also, through inductive analysis, for understanding what they considered to be the top priorities for improving science communication and the presentation of scientific knowledge. An enquiry is also made into whether there were differences between countries and topics and how the suggestions reflected a particular understanding of public engagement with science. The findings are presented as a citizens’ science communication improvement framework with four main dimensions: accessibility, validity, understanding and engagement. This framework not only highlights the citizens’ multidimensional perception of science communication but can also be used by scientists or science communicators to assess the quality of specific messages or initiatives as to how they answer the needs and demands of the public.