Cloud computing offers organizations scalable storage and computation, but outsourcing data processing to third-party infrastructure introduces serious privacy and confidentiality risks. Two complementary paradigms have emerged to address this challenge: homomorphic encryption (HE), which allows computation directly on encrypted data, and federated learning (FL), which enables collaborative model training without centralizing raw data. This paper presents a structured review of privacy-preserving data processing techniques for cloud environments built on HE and FL, individually and in hybrid combination. We propose a taxonomy of existing approaches, synthesize representative literature in a comparative table, illustrate a generic hybrid HE-FL architecture, and evaluate the two paradigms against criteria including data exposure, computational overhead, communication cost, resistance to inference attacks, and cloud deployment readiness. We further identify open challenges — including computational latency, key management, non-IID data distributions, and standardization gaps — and outline promising directions for future research, such as hardware-accelerated HE, adaptive encryption granularity, and standardized hybrid privacy frameworks for cloud-native machine learning.