Semantic communication (SemCom) emerges as a transformative paradigm for traffic-intensive visual data transmission, shifting focus from raw data to meaningful content transmission and relieving the increasing pressure on communication resources. However, to achieve SemCom, challenges are faced in accurate semantic quantization for visual data, robust semantic extraction and reconstruction under diverse tasks and goals, transceiver coordination with effective knowledge utilization, and adaptation to unpredictable wireless communication environments. In this paper, we present a systematic review of SemCom for visual data transmission (SemCom-Vision), wherein an interdisciplinary analysis integrating computer vision (CV) and communication engineering is conducted to provide comprehensive guidelines for the machine learning (ML)-empowered SemCom-Vision design. Specifically, this survey first elucidates the basics and key concepts of SemCom. Then, we introduce a novel classification perspective to categorize existing SemCom-Vision approaches as semantic preservation communication (SPC), semantic expansion communication (SEC), and semantic refinement communication (SRC) based on communication goals interpreted through semantic quantization schemes. Moreover, this survey articulates the ML-based encoder-decoder models and training algorithms for each SemCom-Vision category, followed by knowledge structure and utilization strategies. Finally, we discuss potential SemCom-Vision applications.