This chapter introduces the puzzles raised by the existing literature relating to competence in public opinion, valence, partisanship, party competition and vote choices, and summarises the three concepts of public opinion about competence demonstrated throughout the book. Those concepts are (i) issue ownership – a positive handling reputation via the representation by parties of different issue-publics and constituencies; (ii) issue performance – the degree to which a policy is going well or going badly for the party in office; and (iii) generalised competence – the degree to which parties are trusted across the policy agenda. It identifies the theoretical questions that can be tackled by thinking about competence in these ways: what explains changes in issue ownership? Does policy performance matter, and if so, for which issues and parties? Why do governing parties so regularly lose support? How, when and why does competence matter in elections? The chapter explains the analytic approach of the book which assesses variation in public opinion over time, across parties, periods of government, across countries and across policy issues.