Generative Artificial Intelligence (GenAI) enables machine learning systems to generate realistic text, images, audio, and video, driving widespread adoption across multiple industries. However, the internal decision-making processes of generative models remain largely opaque, limiting interpretability and undermining user trust. Although outputs may appear accurate at a surface level, they can reflect biased or misaligned information, raising concerns about ethical, medical, and social acceptability. Existing explainability techniques for GenAI are still immature and largely adapted from methods designed for deterministic predictive models, such as those used in finance and risk analysis. While effective in those domains, these approaches fail to capture generative-specific phenomena, including latent-space dynamics and probabilistic generation, resulting in predominantly surface-level explanations. To address these limitations, this study conducts a systematic analytical review of GenAI explainability techniques and introduces an Incremental Transparency Perspective, which frames explainability as a continuous and cumulative optimization process across the GenAI lifecycle. Empirical trend analysis reveals structural gaps and architecture-dependent limitations in current approaches, underscoring the need for measurable, stakeholder-centered, and architecture-aware explainability frameworks. Together, these contributions establish a foundation for developing trustworthy, accountable, and deployable GenAI systems.