As wireless communication becomes an ever-more important and pervasive part of our everyday life, system capacity and quality of service issues are becoming more critical. In order to increase the system capacity and improve the quality of service, it is necessary that we pay closer attention to bandwidth and power efficiency issues. Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation technique for high speed data transmission and is generally regarded as bandwidth efficient. However, OFDM signals suffer from high peak-to-average power ratios (PARs) which lead to power inefficiency in the RF portion of the transmitter. Moreover, in OFDM, the well-known pilot tone assisted modulation (PTAM) technique utilizes a number of dedicated training pilots to acquire the channel state information (CSI), resulting in somewhat reduced bandwidth efficiency. In this dissertation, we will address the above mentioned bandwidth and power efficiency issues in wireless transmissions. To avoid bandwidth efficiency loss due to dedicated training, we will first develop a superimposed training framework that can be used to track the frequency selective as well as the Doppler shift characteristics of a channel. Later on, we will propose a generalized superimposed training framework that allows improved channel estimates. To improve the power efficiency, we adopt the selected mapping (SLM) framework to reduce the PARs for both OFDM and forward link Code Division Multiple Access (CDMA). We first propose a dynamic SLM algorithm to greatly reduce the computational requirement of SLM without sacrificing its PAR reducing capability. We propose a number of blind SLM techniques for OFDM and for forward link CDMA; they require no side information and are easy to implement. Our proposed blind SLM technique for OFDM is a novel joint channel estimation and PAR reduction algorithm, for which bandwidth efficiency power efficiency - complexity - bit error rate tradeoffs are carefully considered.