Varying length patterns extracted from speech and image data correspond to sets or sequences of local feature vectors. Kernels designed for varying length patterns are called as dynamic kernels. This Chapter presents the issues in designing the dynamic kernels, different methods for designing the dynamic kernels, and the suitability of dynamic kernels based approaches to speech and image processing tasks. We explore the matching based approaches to designing dynamic kernels for speech and image processing tasks. An intermediate matching kernel (IMK) for a pair of varying length patterns is constructed by matching the pairs of local feature vectors selected using a set of virtual feature vectors. For varying length patterns corresponding to sets of local feature vectors, a Gaussian mixture model (GMM) is used as the set of virtual feature vectors. The GMM-based IMK is considered for speech processing tasks such as speech emotion recognition and speaker identification, and for image processing tasks such as image classification, image matching and image annotation in content-based image retrieval. For varying length patterns corresponding to sequences of local feature vectors, a hidden Markov model (HMM) is used for selection of local feature vectors in constructing the IMK. The HMM-based IMK is considered for speech recognition tasks such as E-set recognition and Consonant-Vowel (CV) unit recognition. We present the studies comparing the IMK based ap-proaches and the other dynamic kernels based approaches. © 2017 by World Scientific Publishing Co. Pte. Ltd.