Density estimation is a fundamental research area in statistics and machine learning focused on modeling the underlying probability distribution of data, enabling tasks such as anomaly detection, generative modeling, and data synthesis. Traditional approaches include parametric methods like Gaussian and mixture models, and non-parametric methods such as kernel density estimation (KDE) and nearest-neighbor-based estimators. Recent research has expanded to deep learning-based techniques, including normalizing flows, autoregressive models, variational autoencoders (VAEs), and energy-based models, which allow flexible, high-dimensional density estimation with scalable training. Applications span anomaly detection, image and video generation, natural language modeling, and scientific data analysis, where accurately capturing complex distributions is critical. Current studies also focus on improving estimation efficiency, robustness to high-dimensional and sparse data, and integration with semi-supervised and unsupervised learning frameworks, establishing density estimation as a core tool for probabilistic modeling in modern AI systems.