Machine learning has become a transformative force in VLSI design and semiconductor manufacturing. This study provides a critical review of state-of-the-art ML approaches from across the digital IC design flow (from HLS, via RTL PPA prediction, to logic synthesis, placement, routing, verification, DFT, and test), and major semiconductor manufacturing domains, such as lithography, etch modeling, metrology, defect classification, yield prediction, and equipment health monitoring. This study provides comparative insights, cross-domain analysis, and taxonomy-driven organization for ML methods such as supervised learning, GNNs, RL, AutoML, generative AI, PINNs, and LLM-based approaches. There is the bottlenecks-domain shift, data scarcity, compute cost, and explainability identified -and put forward a future roadmap that includes hybrid physics-ML modeling, industrial-scale datasets, explainable models, and ML-driven digital twins. This systematic synthesis shows that ML is transforming EDA workflows and making next-generation semiconductor manufacturing intelligence achievable