The rapid evolution of wireless networks is driven by the growth of wireless packet data applications such as interactive mobile multimedia applications, wireless streaming services, and video-on-demand. The largely heterogeneous network structures, severe channel impairments, and complex traffic patterns make the wireless networks much more unpredictable compared to their wired counterparts. One of the major challenges with the roll-out of these services is therefore the design of wireless networks that fulfill the stringent quality of service requirements of mobile multimedia applications. In this tutorial, we provide a survey on the evolution of quality of experience (QoE) concepts in the context of mobile multimedia systems touching on the past, present, and future aspects. Specifically, the ideas behind QoE are discussed and an overview of related standardization work and major research initiatives is provided. On this basis, QoE metrics for speech, image, and video are described. Given the increase on visual services, perceptual image and video quality metrics for real-time quality assessment of mobile multimedia experience are discussed. This includes a classification of quality assessment methods, comparison of psychophysical versus engineering approaches, perceptual image and video quality assessment, and some example applications. An outlook on future work and challenges is also provided.