In the aftermath of the financial and economic crisis, large shares of working-age individuals in Ireland either did not work or only to a limited extent. As the labour-market recovery gathered pace during 2013, 32% were without employment during the entire year, and a further 14% had weak labour-market attachment, working only a fraction of the year, or on restricted working hours. This paper applies a novel method for measuring and visualising employment barriers of individuals with no or weak labour-market attachment, using household micro-data. It first develops indicators to quantify employment obstacles under three broad headings: (i) work-related capabilities, (ii) incentives, and (iii) employment opportunities. It then uses these indicators in conjunction with a statistical clustering approach to identify unobserved ("latent") groups of individuals facing similar combinations of barriers. The resulting typology of labour-market difficulties provides insights on the most pressing policy priorities in supporting different groups into employment. A detailed policy discussion illustrates how the empirical results can inform people-centred assessments of existing labour-market integration measures and of key challenges across different policy areas and institutions. The most common employment obstacles in Ireland were limited work experience, low skill levels, and scarce job opportunities. Although financial disincentives, health problems and care responsibilities were less widespread overall, they remained important barriers for some groups. A notable finding is that just under 40% of jobless or low-intensity workers face three or more simultaneous barriers, highlighting the limits of narrow policy approaches that focus on subsets of these employment obstacles in isolation.