In this talk we will describe two models for the theory of infinity-operads: Lurie's model and the simplicial lists model (developed in joint work with Özgün Ünlü). We begin by briefly introducing operads as a categorical tool to control and study a variety of algebraic structures. As it is known that higher dimensional categorical structures are presentation-sensitive, different ways of thinking about ordinary operads lead to different formulations of a higher variant. Lurie's model is based on the notion of operator category, while the simplicial lists model is based on a nerve theorem related to the monoidal envelope associated to an operad. Time permitting, we will discuss how the two can be related to each other.