This chapter discusses the state of the art and current investigations by the authors in the field of perceptual haptic coding. The discussion covers both kinesthetic and tactile codecs, which take different types of input and target different objectives. Kinesthetic codecs are designed to reduce the number of packets to be exchanged bidirectionally during network-based physical interaction. Bilateral teleoperation of a robotic system with force feedback is an example for this. A special requirement in this context is to ensure stability and reduce data traffic despite the negative impact of delay in the bidirectional exchange of kinesthetic information. For this purpose, we marry kinesthetic data reduction schemes with stabilizing control approaches and thereby improve the trade-off between stability, transparency, and network resource usage. Tactile codecs are designed to minimize the required transmission rate during unidirectional exchange of surface interaction information. Compared to the kinesthetic codecs they are more delay-tolerant. Both types of haptic codecs share the need to incorporate mathematical models of human perception. The development of such models is a current research challenge. To this end, we describe the most widely used models of human kinesthetic and vibrotactile perception and how they can be leveraged in perceptual coding schemes. Additionally, haptic codecs need to support multiple points of interaction. This requires a hierarchical design, where spatial redundancy (e.g., on a finger, among fingers, across the hand, arm, etc.) is exploited. Finally, haptic codecs need to be learning-oriented, which means that they need to support remote learning scenarios, such as learning from (remote) demonstrations. We also describe and analyze the performance of the kinesthetic and tactile codecs under consideration within the IEEE standardization activity P1918.1.1. We present both objective and subjective evaluation results and complement the chapter with a discussion of the available objective quality measures that have been found to accurately predict human judgments of compressed haptic signals. The development of haptic codecs requires interdisciplinary expertise from psychology, signal processing, applied information theory, control, and sensor/actuator development. Haptic codecs are a key enabler for a wide range of applications, e.g., in industry or medicine.