The extreme learning machine (ELM) introduced by Huang et al. is a learning algorithm designed based on the generalized SLFNs with a wide variety of hidden nodes. It randomly generates hidden node parameters and then determines the output weights analytically. ELM is very simple and it tends to obtain the smallest training error and the smallest norm of weights, which can lead to good generalization performance of networks. However, the good performance of ELM is valid only when the network architecture is chosen correctly. This thesis investigated the problems of network architecture design and model selection of ELM. Essentially, in the thesis, we proposed the use of network ensemble to improve the generalization performance of online ELM network and then we focused on the novel constructive approaches to alter the network structure during the learning process in order to find the appropriate architecture. A parsimonious structure can be found by the constructive method with a backward refinement phase.