Ireland is the only country in Europe with a direct question in its Labour Force Survey to identify minimum wage employees. By combining this with the longitudinal component of the Labour Force Survey, we examine the labour market transitions of minimum wage employees over a period of up to five quarters. After one quarter, just over half of minimum wage employees are still on minimum wage while 28 percent have moved to higher pay. After one year, almost half have moved to higher pay, with just one-third remaining on minimum wage. Employees that move to higher pay are more likely to change jobs compared to those that stay on minimum wage. Despite this, the majority (almost 90 percent) of minimum wage employees that transition to higher pay do so with the same employer. We employ a dynamic random effects probit model to estimate the degree of genuine state dependence of minimum wage employment. While there is some degree of true state dependence, much of the persistence in minimum wage employment is due to observed and unobserved heterogeneity, whereby minimum wage employees possess characteristics that result in them entering, and staying on, minimum wage. Our results also indicate that minimum wage employees are about five times more likely than higher paid employees to transition into economic inactivity. However, the majority of these are young people in education, and as such may not be overly concerning to policymakers.