We consider a point-to-point communication system in which data packets randomly arrive to a finite-length buffer and are subsequently transmitted to a receiver over a timevarying wireless channel. Data packets are subject to loss due to buffer overflow and transmission errors. We study the problem of adapting the transmit power and rate based on the buffer and channel conditions so that the system throughput is maximized, subject to an average transmit power constraint. Here, the system throughput is defined as the rate at which packets are successfully transmitted to the receiver. We consider this buffer/channel adaptive transmission when only incomplete system state information is available for making control decisions. Incomplete system state information includes delayed and/or imperfectly estimated channel gain and quantized buffer occupancy. We show that, when some delayed but error-free channel state information is available, optimal buffer/channel adaptive transmission policies...