Sentiment Analysis, or opinion mining, is the computational study of opinions, sentiments, emotions, and attitudes expressed in texts. Due to the rapid expansion of social media, e-commerce platforms, and digital communication, huge amount of opinion rich information is generated daily. This tremendous surge has also substantially increased the importance of sentiment analysis for understanding public opinion, monitoring brand image, forecasting market trend and enhancing customer relations. This paper also offers a detailed survey of SA methods, from classic lexicon-based methods to recent deep learning models and transformers such as BERT and RoBERTa. We test their effectiveness on benchmark datasets with empirical experiments and discuss their pros and cons in various real-world scenarios. Beyond these popular approaches, we present a range of domain-specialized techniques, multilingual processing, and hybrid architectures synthesizing symbolic and statistical methods. We empirically show that the transformer models outperform LR, SVM, LSTM and BERT on the IMDB dataset in achieving better understanding of context-specific nuances. We next provide a number of problematic applications of sentiment analysis including sarcastic expression detection, domain adaptation, data unbalance and sentiment ambiguity. Various application scenarios in marketing, healthcare, finance and politics are also included in the paper. Finally, we describe future research avenues focusing on explainable sentiment models, real-time analysis systems, and multimodal fusion approaches that take into account text, audio and visual features.The goal of this study is to provide researchers and practitioners with a fundamental framework for creating sentiment analysis systems that are intelligent, scalable, and reliable.