This paper proposes the Modular Machine Learning (MML) paradigm to address the limitations of large-scale language models (LLMs) in terms of explainability, reliability, adaptability, and scalability. MML decomposes the complex structure of LLMs into three interdependent components: modular representations, modular models, and modular reasoning. This decomposition clarifies the internal workings of LLMs, enables flexible and task-adaptive model design, and facilitates interpretable and logic-driven decision-making processes. This paper presents a feasible implementation of MML-based LLMs utilizing advanced techniques such as disjoint representation learning, neural architecture search, and neural symbolic learning. Key challenges, such as the integration of continuous neural and discrete symbolic processes, joint optimization, and computational scalability, are addressed, along with future research directions. Ultimately, the integration of MML and LLMs is expected to bridge the gap between statistical (deep) learning and formal (logical) reasoning, paving the way for robust, adaptable, and reliable AI systems in a variety of real-world applications.