Speech summarization is typically performed by using a cascade of speech recognition and text summarization models. End-to-end modeling of speech summarization models is challenging due to memory and compute constraints arising from long input audio sequences. Recent work in document summarization has inspired methods to reduce the complexity of self-attentions, which enables transformer models to handle long sequences. In this work, we introduce a single model optimized end-to-end for speech summarization. We apply the restricted self-attention technique from text-based models to speech models to address the memory and compute constraints. We demonstrate that the proposed model learns to directly summarize speech for the How-2 corpus of instructional videos. The proposed end-to-end model outperforms the previously proposed cascaded model by 3 points absolute on ROUGE. Further, we consider the spoken language understanding task of predicting concepts from speech inputs and show that the proposed end-to-end model outperforms the cascade model by 4 points absolute F-1.