In the design of next generation multiuser communication systems, multiple antenna transmission is an essential part providing spatial multiplexing gain and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. To this effect we propose two independent approaches for an efficient representation of the channel in multiuser MIMO systems. In the first approach, channel quantization is considered where the total number of feedback bits is limited. A resource allocation scheme is proposed where the available rate is split between the scheduling phase, where all users feed back a coarse CSI quantization, and the precoding phase where the selected receivers refine their CSI. The optimum splitting of the available feedback rate provides a large increase in performance and even simple heuristic splitting gives a noticeable advantage. In the second approach, we exploit a combination of instantaneous and statistical channel information. For spatially correlated Rayleigh and Ricean channels, it is shown that the CSI to large extent can be represented by the channel norm when the long-term channel statistics are known. Within a minimum mean square error (MMSE) estimation framework, feedback of a few bits of the quantized channel norm is sufficient to perform efficient resource allocation and achieve performance close to that of full CSI.