Faster computing and higher available bandwidths for digital communications have made visual communications increasingly possible - one- and two-way exchange of both images and video, including browsing multimedia databases, real-time imaging, and video-conferencing. Advances in image and video compression have contributed to the feasibility of visual communications, and packet networks such as today's ATM and future wireless ATM networks can offer the required bandwidths. However, these networks cannot offer guaranteed packet delivery - some data can be lost. As such, these networks cannot be used to reliably deliver visual information coded using today's compression standards. The goal of this research is to provide reliable visual communications over unreliable packet networks with dynamic bandwidths and packet handling characteristics through source coding specialized to transmission over such networks. This research involves developing specialized image and video compression techniques for transmission over networks with dynamic bandwidths and packet handling characteristics. Traditionally to deal with loss in transmission, redundancy is completely removed from data via source coding and then reinserted through channel coding, following Shannon's joint source-channel coding theorem. This research investigates redundant source coding, in which redundancy is included in the source coding so that less or no channel coding is required, while achieving better visual quality than if the joint-source channel coding theorem is applied. Specifically, redundant source coding techniques for subband-wavelet image representations and for the temporal information in video sequences are being developed, along with suitable packetization strategies. Optimal data partitioning algorithms are also being developed, to allow transmission over multiple sub-channels with different characteristics.