Multi-input and multi-output (MIMO) and orthogonal frequency division multiplexing (OFDM) have attracted significant attention, and become promising techniques for high data rate wireless communication systems. They have been widely studied and employed for 4G systems such as WiFi, DVB-T, WiMAX and LTE-A. Hence, the performances of such systems are critical to practical applications including online gaming, files transfer and high quality video streaming et al. The thesis have studied low-complexity channel estimation and detection techniques to improve the reliability of the wireless links or increase the spectral efficiency at low cost as follows. (1) MIMO-OFDM systems over slowly varying channels. Conventional comb-type uniform pilot allocation (UPA) for MIMO-OFDM systems employed by many standards obtains reliable channel estimates in the sense that the pilots occupy the subcarriers only for channel estimation without any further benefit. To make better use of pilots for MIMO- OFDM systems to acquire an additional performance gain, a novel receiver based dy- namic pilot allocation (DPA) scheme is proposed with the aid of a feedback link. The DPA inserts pilots into most faded subcarriers at expense of moderate MSE performance degradation in channel estimation. (2) Narrow band MIMO systems. High spectral efficiency can be achieved by a large size of transmit and receive antennas, but the BER performance of conventional linear and successive interference cancellation (SIC) receivers cannot be comparable to max- imum likelihood (ML) receivers. Although one alternative method (real-valued sphere decoder) can approach the performance of ML receivers with near SIC complexity at high SNR, it cannot efficiently process phase shift keying (PSK) modulation. On the other hand, the complex-valued sphere decoder can process PSK, but with complicated enumeration. Hence, a SIC based complex-valued sphere decoder is proposed with prob- abilistic tree pruning. The proposed complex-valued SD can reduce the tree span and save the complexity induced by enumeration schemes. Additionally, the basic principles of complex-valued sphere decoder can be naturally extended to an instantaneous union bound estimation for ML receivers. Its complexity is significantly reduced. However, the initial radius and candidates bound for the union bound estimation have not been studied, which have significant influences on the search complexity. Hence, a channel statistics based initial radius is derived based on the Rayleigh-Ritz theorem and the probability den- sity function (PDF) of the channel matrix. The candidates bound can also be computed by the initial radius or the updated radius to reduce the tree span as the sphere decoder does. (3) OFDM systems over rapidly time-varying channels. Inter-carrier interference (ICI) becomes the bottleneck for the OFDM systems over rapidly time-varying channels. The complexity of equalization for such scenarios will be high if a full matrix inversion is em- ployed in the receivers, because the number of subcarriers for existing standards is beyond several hundred. To avoid a full matrix inversion, two novel matched filter (MF) based ICI cancellation algorithms have been proposed to mitigate the dominating ICI coeffi- cients inside the banded channel matrix. In addition, a multi-segmental iterative channel estimation technique splits one OFDM symbol into several small segments by partial fast Fourier transform (PFFT), and obtains the channel impulse response estimates for seg- ments. One can linearly interpolates the time-varying channels between segments with low complexity. It is found that the MF based ICI cancellation algorithms, incorporating multi-segmental iterative channel estimation are robust to the time variation.