With the fast adoption of IP-based communications for mobile computing, users are expecting a similar service in wireless and wired networks. This raises the need for setting guarantees to the quality of the offered service (QoS), despite the technology of the access network (AN) or the mobility of the terminal. As mobile computing is getting more popular on a daily basis, new broadband cellular wireless ANs will appear with overlapping coverage in hot spots. This generates a new challenge for QoS provision, as it will have to deal with fast mobility of terminals. Various QoS architectures have been defined, but none provides full support for guaranteed service levels for mobile hosts (MHs). This paper discusses the problems related to providing QoS to MHs and identifies the existing solutions and future work needed.