Internet video (mainly transported over TCP) is now about 40 percent of consumer Internet traffic and it continues to grow. Research in the field of multimedia streaming applications including for example video-on-demand (VOD), multimedia sharing, and Internet live broadcasting has been ongoing for many years. In the recent past, more and more multimedia streams have been distributed over application-layer multicast (ALM) and peer to peer (P2P) networks. Due to the heterogeneous nature of IP networks and communication nodes, the effective delivery of media streams is still facing many challenges. With the wide use of multimedia communications applications, resources such as buffer, memory or storage of nodes and Internet bandwidth are often scarce. In this work, we study optimal and distributed resource allocation for time-sensitive and bandwidth-demanding multimedia applications, in particular, P2P multicast streaming applications. To accommodate the variability of streaming rates and packet delays, buffers store streamed packets before sending them smoothly to the player. While receiver buffers are used for small time-scale rate and packet delay fluctuations (on the order of tens of round trip time (RTT)), rate control protocols are used to adapt the sending rate on a long time-scale. Therefore, we consider two research problems: 1) given the required buffer overflow and underflow probability constraints, what is the optimal buffer size and how should we set the initial buffering delay given network conditions such as packet loss rate and RTT? 2) given the available bandwidth in the network, how should we optimally allocate the streaming rate in a distributed manner to optimize the overall streaming quality perceived by all receiving nodes?The first main contribution is that we have developed an analytical framework for TCP streaming. To this end, we propose a TCP congestion window model and find the distribution of TCP window bounds which is critical for the underflow and overflow probability of TCP streaming buffer. Based on this analytical framework for TCP streaming, we provide systematic guidelines for buffer sizing and buffer delay to meet the required buffer overflow probability, underflow probability and low delay in various network conditions. The analytical framework is further extended for P2P multicast streaming. We evaluate our framework by extensive simulations in ns-2 and practical experimentations of P2P multicast streaming in real networks.The second main contribution is the extension of the utility-price model for P2P multicast systems and the formulation of an optimization problem for rate allocation to maximize the aggregate utilities for the receivers. To solve the optimization problem, we have designed distributed rate control algorithms, namely a novel algorithm for the primal problem and a dual algorithm for the transformed problem. We have evaluated the performance of the designed two algorithms; the properties of the two algorithms are: 1) they maximize the overall streaming quality for scalable video streams in the tree; 2) they are friendly to coexisting TCP traffic (for this, we extend the concept of TCP-friendliness for unicast to TCP-friendliness for applicationlayer multicast); 3) the dual algorithm converges with oscillations whereas the primal algorithm always returns a feasible and stable solution, avoiding oscillations during convergence. 4) and, most importantly, our algorithms are fully distributed and competitive with respect to messaging overhead.