I think the technical aspects of building the necessary communication infrastructure for a human trip to Mars would be absolutely fascinating. Due to the large RTTs (varying from 4 to 24 minutes), use of TCP/IP on Earth-Mars links is infeasible. Instead, you'd have two TCP/IP Internets (Earth's Internet and Mars's Internet), with store-and-forward protocols being used between them [1].
Earth is only a small point from Mars and vice versa. There is an upper limit of what you can send via direct electromagnetic radiation. However, you can set up relay stations in the solar system. It will increase the RTTs for those data but also increase the available bandwidth. You'll likely have a layered internet where really fast communication is most expensive, and it gets cheaper the slower you allow it to be, down to the slowest (but highest bandwidth) method of your data being printed into DNA (or some other high density storage medium) and put onto the next scheduled transport to Earth.