We present a detailed study of the part of the Web related to media content, i.e., the Media Web. Using publicly available data, we analyze the evolution of incoming and outgoing links from and to media pages. Based on our observations, we propose a new class of models for the appearance of new media content on the Web where different \textit{attractiveness} functions of nodes are possible including ones taken from well-known preferential attachment and fitness models. We analyze these models theoretically and empirically and show which ones realistically predict both the incoming degree distribution and the so-called \textit{recency property} of the Media Web, something that existing models did not do well. Finally we compare these models by estimating the likelihood of the real-world link graph from our data set given each model and obtain that models we introduce are significantly more likely than previously proposed ones. One of the most surprising results is that in the Media Web the probability for a post to be cited is determined, most likely, by its quality rather than by its current popularity.