This article presents the results of research conducted over the period 2010-2012 in Estonia with the aim of identifying the expectations for the quality of higher education by principal parties in higher education, the state, the market and academia, as well as describing the differences and similarities in their expectations. The findings show that the interpretations and expectations of different parties in higher education differ noticeably. It became evident that the market has the most balanced view valuing almost equally input, process and output characteristics, although the greatest emphasis is placed on inputs. The state and academia also emphasise processes and inputs but somewhat less outputs. Students focus on process and input characteristics only. The article details the approaches to "a good university" by different stakeholders and discusses possibilities of considering the different expectations when further developing the external quality evaluation system.