We review methods for capturing differential coexpression, which can be divided into two cases by the size of gene sets: 1) two paired genes and 2) multiple genes. In the first case, two genes are positively and negatively correlated with each other under one and the other conditions, respectively. In the second case, multiple genes are coexpressed and randomly expressed under one and the other conditions, respectively. We summarize a variety of methods for the first and second cases into four and three approaches, respectively. We describe each of these approaches in detail technically, being followed by thorough comparative experiments with both synthetic and real data sets. Our experimental results imply high possibility of improving the efficiency of the current methods, particularly in the case of multiple genes, because of low performance achieved by the best methods which are relatively simple intuitive ones.