In the post-GWAS era, colocalization testing has been playing an increasingly important role in inferring causal genetic variants and genes from GWAS trait-associated loci. However, colocalization testing is challenging. We first discuss some severe limitations of the existing methods, thus motivating our development of a general and powerful method. We develop a simple and general approach based on conditional analysis of a locus on multiple traits. We use extensive simulations to demonstrate the advantages of our method over existing methods. We apply our and other methods (when possible) for colocalization analyses of multiple correlated GWAS traits and that of a GWAS trait and gene expression.