The development of cloud, fog, and edge computing has led to great advances in reducing latency and saving bandwidth, and these methods have therefore been broadly applied in various domains, including healthcare, transportation, and the Internet of Things (IoT). Traditional edge computing solutions have proven to be insufficient in fulfilling the demanding prerequisites of low latency and high data rates. Additionally, publicly available edge cloud solutions fail to meet the required standards for ensuring privacy protection. Consequently, Private Edge Cloud Systems (PECSs) have garnered attention as a prospective solution owing to their capacity to mitigate privacy risks and their significant computing capacity. PECS research has seen significant growth, but there is a lack of detailed review of its issues, approaches, and applications in the literature. To explore the potential application value of PECS, this paper provides a systematic review of intelligent platforms and architecture for PECSs. Specifically, an overview of the fundamental characteristics of PECSs is provided. Second, we classify intelligent platforms and architectures and analyze their implementation techniques and realization methods. Third, we discuss four specific application scenarios. Finally, promising future research directions are discussed. The findings of this research show that PECSs can effectively meet the requirements for low latency and privacy protection and are a fertile domain for further research.