This paper addresses a new kernel learning problem, referred to as ‘asymmetric kernel learning’ (AKL). First, we give the definition of asymmetric kernel and point out that many ‘similarity functions’ in real applications can be viewed as asymmetric kernels, for example, VSM, BM25, and LMIR in search. Then, we formalize AKL as an optimization problem whose objective function is a regularized loss function on supervised training data. Next, we propose an approach to AKL, which conducts AKL by using kernel methods. In the approach, the space of asymmetric kernels is assumed to be a reproducing kernel Hilbert space (RKHS), and thus existing kernel methods can be employed to learn the optimal asymmetric kernel. We also show that such an RKHS (i.e., space of asymmetric kernels) exists and refer to the kernel generating the RKHS as ‘hyper asymmetric kernel’ (HAK). We present examples of HAK as well as theoretical basis for constructing HAKs. The proposed approach is applied to search to learn a relevance model from click-through data. Experimental results on web search and enterprise search data show that the model, named ‘Robust BM25’ can work better than BM25 because it can effectively deal with the term mismatch problem which plagues BM25.