Optical remote sensing images used for Earth surface observations are constantly contaminated by cloud cover. Clouds dynamically affect the applications of optical data and increase the difficulty of image analysis. Therefore, cloud is considered as one of the sources of noise in optical image data, and its detection and removal need to be operated as a pre-processing step in most remote sensing image processing applications. This thesis investigates the current cloud detection and removal algorithms and develops three new cloud removal methods to improve the accuracy of the results. A thin cloud removal method based on signal transmission principles and spectral mixture analysis (ST-SMA) for pixel correction is developed in the first contribution. This method considers not only the additive reflectance from the clouds but also the energy absorption when solar radiation passes through them. Data correction is achieved by subtracting the product of the cloud endmember signature and the cloud abundance and rescaling according to the cloud thickness. The proposed method has no requirement for meteorological data and does not rely on reference images. The experimental results indicate that the proposed approach is able to perform effective removal of thin clouds in different scenarios. In the second study, an effective cloud removal method is proposed by taking advantage of the noise-adjusted principal components transform (CR-NAPCT). It is found that the signal-to-noise ratio (S/N) of cloud data is higher than data without cloud contamination, when spatial correlation is considered and are shown in the first NAPCT component (NAPC1) in the NAPCT data. An inverse transformation with a modified first component is then applied to generate the cloud free image. The effectiveness of the proposed method is assessed by performing experiments on simulated and real data to compare the quantitative and qualitative performance of the proposed approach. The third study of this thesis deals with both cloud and cloud shadow problems with the aid of an auxiliary image in a clear sky condition. A new cloud removal approach called multitemporal dictionary learning (MDL) is proposed. Dictionaries of the cloudy areas (target data) and the cloud free areas (reference data) are learned separately in the spectral domain. An online dictionary learning method is then applied to obtain the two dictionaries in this method. The removal process is conducted by using the coefficients from the reference image and the dictionary learned from the target image. This method is able to recover the data contaminated by thin and thick clouds or cloud shadows. The experimental results show that the MDL method is effective from both quantitative and qualitative viewpoints.