We will first discuss fundamental concepts of phase transition phenomenology in the context of cavity QED systems. A short introduction to cavity QED will be presented. This includes the description of our laboratory setup at Wigner RCP. Then we will describe two recent experiments where first-order phase transitions have been observed with laser cooled and trapped atoms in an optical cavity. Besides the time-resolved observation of the dynamical transmission blockade breakdown phase transition, the system allows for the quantification of enhanced fluctuations in the critical region and for performing finite size scaling measurements.