The convergence of heterogeneous wireless networks and cooperation of mobile nodes with perception, learning and cognitive ability are important characteristics of next generation Cognitive Mobile Internet (CMI). The content-rich multimedia streaming will be the most attractive services in the future wireless network. In this paper, we discussed the challenges and issues as well as future trends on multimedia streaming development in CMI. The focuses include: (i)Cognitive users' needs and behaviors modeling for intelligent video streaming business analysis; (ü)Cross-layer optimized mobile peer-to-peer network for large-scale video resources sharing; (iii) Cognitive transport layer protocol with ability of spectrum and routing perception, real-time multimedia transmission control, and concurrent multipath transfer for multi-spectral channels; (iv)Cognitive routing protocol for adapting to dynamic CMI topology, routing and resource changes. The proposed research structure aims to improve overall system performance and achieve high users' Experience of Quality for multimedia streaming service in future mobile internet.