This paper provides an introductory tutorial for the Interspeech07 special session on “Structure-Based and Template-Based Automatic Speech Recognition”. The purpose of the special session is to bring together researchers who have special interest in novel techniques that are aimed at overcoming weaknesses of HMMs for acoustic modeling in speech recognition. Numerous such approaches have been taken over the past dozen years, which can be broadly classified into structured-based (parametric) and template-based (non-parametric) ones. In this paper, we will provide an overview of both approaches, focusing on the incorporation of long-range temporal dependencies of the speech features and phonetic detail in speech recognition algorithms. We will provide a high-level survey on major existing work and systems using these two types of “beyond-HMM” frameworks. The contributed papers in this special session will elaborate further on the related topics.