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This paper presents a comparative theoretical analysis of Long Short-Term Memory (LSTM) networks and Transformer models for financial volatility forecasting, with specific applications to the CBOE Volatility Index (VIX) and cryptocurrency markets (Bitcoin, Ethereum). Unlike existing empirical comparisons that focus solely on forecast accuracy metrics such as RMSE or QLIKE, this study examines architectural assumptions, training requirements, sample efficiency, interpretability, and theoretical suitability under different market regimes. We find that LSTMs offer superior sample efficiency (500–1,000 observations) and interpretability for low-frequency (daily) volatility forecasting in stationary regimes, while Transformers excel at capturing long-range dependencies (beyond 200 lags) and regime shifts, particularly in high-frequency cryptocurrency data (hourly or minute-level). However, Transformers require substantially more data (10,00050,000 observations) and computational resources, making them impractical for smaller datasets. We propose a hybrid LSTM-attention framework that balances both approaches and identify open research problems including rough volatility integration, real-time attention mechanisms, and attention weight calibration. This review provides actionable guidance for quantitative researchers and practitioners selecting between these architectures for volatility forecasting tasks. Keywords: Volatility forecasting, LSTM, Transformer, attention mechanism, VIX, cryptocurrency, comparative theoretical analysis, long memory, regime shifts.