Federated Learning (FL) has emerged as a transformative distributed learning paradigm that enables collaborative model training without sharing raw data, thereby preserving privacy across large, diverse, and geographically dispersed clients. Despite its rapid adoption in mobile networks, IoT systems, healthcare, finance, and edge intelligence, FL continues to face several persistent and interdependent challenges that hinder its scalability, efficiency, and real-world deployment. In this survey, we present a systematic examination of six core challenges in federated learning: heterogeneity, computation overhead, communication bottlenecks, client selection, aggregation and optimization, and privacy preservation. We analyze how these challenges manifest across the full FL pipeline, from local training and client participation to global model aggregation and distribution, and examine their impact on model performance, convergence behavior, fairness, and system reliability. Furthermore, we synthesize representative state-of-the-art approaches proposed to address each challenge and discuss their underlying assumptions, trade-offs, and limitations in practical deployments. Finally, we identify open research problems and outline promising directions for developing more robust, scalable, and efficient federated learning systems. This survey aims to serve as a comprehensive reference for researchers and practitioners seeking a unified understanding of the fundamental challenges shaping modern federated learning.