Adaptive Bitrate (ABR) video streaming is widely used for over-the-top (OTT) video delivery. Recently, streaming providers have been moving towards using Variable Bitrate (VBR) encodings for the video content, spurred by the potential of improving user QoE (Quality of Experience) and reducing network bandwidth requirements compared to Constant Bitrate (CBR) encodings. However VBR introduces new challenges for ABR streaming, whose nature and implications are little understood. We explore these challenges across diverse video genres, encoding technologies, and platforms. We identify distinguishing characteristics of VBR encodings that impact user QoE and should be factored in any ABR adaptation decision. Traditional ABR adaptation strategies designed for the CBR case are not adequate for VBR. We develop novel best practice design principles to guide ABR rate adaptation for VBR encodings. As a proof of concept, we design a novel and practical control-theoretic rate adaptation scheme, CAVA (Control-theoretic Adaption for VBR-based ABR streaming), incorporating these concepts. Extensive evaluations show that CAVA substantially outperforms existing state-of-the-art adaptation techniques, validating the importance of these design principles.