With the explosive growth of the Internet over the last 10 years, a lot of work has been dedicated to understanding the underlying mechanisms of wired IP traffic. Recently, the rapid deployment of large-scale wireless infrastructures in various environments and the interesting mixture of traffic carried coupled with the large diversity of devices accessing the medium (Cell-phones, Laptops, PDAs) have triggered the attention and curiosity of the research community. This paper analyzes in depth the properties of several large traces of packet data collected between the wireless access point and the IP cloud from an operational wireless service provider. We determine unambiguously the influence of network variables such as the arrival patterns of packet and flows, flow durations and flow interactions, on the aggregate statistics of TCP traffic. In doing so, we highlight the main differences and similarities between wireless and wired IP traffic, and between the two directions (from wireless devices to IP cloud and vice-versa), and show how they can be distinguished. The resulting insights provide a foundation for models of such traffic, necessary for improved resource allocation schemes as well as for the effectiveness of future services and applications.