A desirable goal for cryptographic protocols is to guarantee security when the protocol is composed with other protocol instances. Universally Composable (UC) security provides this guarantee in a strong sense: A UC-secure protocol maintains its security properties even when composed concurrently with an unbounded number of instances of arbitrary protocols. However, many interesting cryptographic tasks are provably impossible to realize with UC security, unless some trusted set-up is assumed. Impossibility holds even if ideally authenticated communication channels are provided. This survey examines and compares a number of set-up assumptions (models) that were recently demonstrated to suffice for constructing UC-secure protocols that realize practically any cryptographic task. We start with the common reference string (CRS) and key registration (KR) models. We then proceed to the "sunspot" models, which allow for some adversarial control over the set-up, a number of models which better captures set-up that is globally available in the system, and a timing assumption. Finally, we briefly touch upon set-up models for obtaining authenticated communication.