Low-latency is a critical user Quality-of-Experience (QoE) metric for live video streaming. It poses significant challenges for streaming over the Internet. In this paper, we explore the design space of low-latency live streaming by developing dynamic models and optimal adaptation strategies to establish QoE upper bounds as a function of the allowable end-to-end latency. We further develop practical live streaming algorithms within the iterative Linear Quadratic Regulator (iLQR) based Model Predictive Control and Deep Reinforcement Learning frameworks, namely MPC-Live and DRL-Live, to maximize user live streaming QoE by adapting the video bitrate while maintaining low end-to-end video latency in dynamic network environment. Through extensive experiments driven by real network traces, we demonstrate that our live streaming algorithms can achieve close-to-optimal performance within the latency range of two to five seconds.