The study of phase transitions in random graphs was initiated by Erdos and Renyi in 1960. They proved among other things that a uniform random graph undergoes a drastic change in the size and structure of the largest component, caused by altering a critical edge density. Since the seminal work of Erdos and Renyi, various random graph models have been introduced and studied over the last five decades. In this talk I will discuss some recent results in phase transitions in random hypergraphs. (Joint work with Oliver Cooley and Christoph Koch.)