Scheduling has always been an indispensable part of resource allocation in wireless networks. Accurate information about channel-state is assumed as a modeling simplification. However, in a real-life network ,e.g., Long Term Evolution(LTE) or IEEE 802.16e WiMAX, the channel-state information feedback to the transmitter can have uncertainty. The primary reason being that although resource allocation is done at the finer granularity of a Physical Resource Block (PRB), channel-state information is still feedback at the coarser granularity of a sub band, which is a group of PRBs. This is done to reduce the feedback traffic from the users to the Base Station. However, this averaging causes information loss and hence, the resulting uncertainty at the scheduler. Moreover, uncertainty might be present in the channel-estimates because of the very process of estimation. In the first part of the thesis, we model the channel-estimate in accuracy and characterize the network stability region. Compared to earlier works, we allow the channel estimates to have dependence among themselves, which is a more realistic situation in a modern LTE or WiMax network. We then propose two simple Max Weight based scheduling schemes that achieve any rate in the interior of the stability region. We also derive an asymptotically tight upper bound on the mean queueing delay in our system under one of the throughput-optimal policies we propose. The above policies ensure stability of the network and we have also obtained bounds on the mean queueing delays. However, different applications may require certain quality of service which may not be satisfied by these policies. Thus, we also propose a throughput-optimal policy for the network under traffic with heterogeneous QoS constraints and present some numerical results studying its performance. In the second part of the thesis, we study the problem of energy-efficient scheduling under average delay constraint. For wireless access technologies, the largest power consumer is the Base Station(BS). Any reduction in the power consumption in a BS will reduce carbon footprint from the Information and Communication Technology sector. We concentrate on the problem of minimizing the total non-renewable power consumed in a Green BS, that is powered by renewable energy sources ,e.g., solar/wind energy and may also be connected to the power grid or diesel generators. Specifically, we consider the problem of minimizing the average grid power consumption of a Green BS downlink in scheduling multiple users with average delay constraints. We have a packetized model for the data packets (i.e., the packets cannot be fragmented) which is a more realistic model for packet-switched networks. The power function is a non-decreasing convex function of the queue-lengths and only one user is allowed to transmit in a slot. We prove the existence of a power optimal policy under delay constraints for multiple users. We analyse the problem and provide some structural results for the optimal policy.