We design throughput-optimal dynamic broadcast algorithms for multi-hop networks with arbitrary topologies. Most of the previous broadcast algorithms route packets along spanning trees. For large time-varying networks, computing and maintaining a set of spanning trees is not efficient, as the network-topology may change frequently. In this paper, we design a class of dynamic algorithms, which make simple packet-by-packet scheduling and routing decisions, and hence obviate the need for maintaining any global topological structures, such as spanning trees. Our algorithms may be conveniently understood as a non-trivial generalization of the familiar back-pressure algorithm for unicast traffic, which performs packet routing and scheduling based on queue lengths. However, in the broadcast setting, due to packet duplications, it is difficult to define appropriate queuing structures. We design and prove the optimality of a virtual queue-based algorithm, where virtual queues are defined for subsets of nodes. We then propose a multi-class broadcast policy, which combines the above scheduling algorithm with in-class-in-order packet forwarding, resulting in significant reduction in complexity. Finally, we evaluate the performance of the proposed algorithms via extensive numerical simulations.