Multimedia transmission over time-varying wireless channels presents a number of challenges beyond existing capabilities conceived so far for third-generation networks. Efficient quality-of-service (QoS) provisioning for multimedia on these channels may in particular require a loosening and a rethinking of the layer separation principle. In that context, joint source-channel decoding (JSCD) strategies have gained attention as viable alternatives to separate decoding of source and channel codes. A statistical framework based on hidden Markov models (HMM) capturing dependencies between the source and channel coding components sets the foundation for optimal design of techniques of joint decoding of source and channel codes. The problem has been largely addressed in the research community, by considering both fixed-length codes (FLC) and variable-length source codes (VLC) widely used in compression standards. Joint source-channel decoding of VLC raises specific difficulties due to the fact that the segmentation of the received bitstream into source symbols is random. This paper makes a survey of recent theoretical and practical advances in the area of JSCD with soft information of VLC-encoded sources. It first describes the main paths followed for designing efficient estimators for VLC-encoded sources, the key component of the JSCD iterative structure. It then presents the main issues involved in the application of the turbo principle to JSCD of VLC-encoded sources as well as the main approaches to source-controlled channel decoding. This survey terminates by performance illustrations with real image and video decoding systems.