The increasing deployment of photovoltaic (PV) systems requires accurate solar energy forecasting to improve grid stability, optimize energy storage, and improve energy management. Traditional solar energy prediction models often require significant computational resources, making them impractical for deployment on edge devices in remote or resource-constrained environments. Tiny Machine Learning (tinyML) is emerging as a promising solution, providing low-power, real-time forecasting capabilities on edge devices. This review comprehensively investigates the application of tinyML models in solar irradiance and PV power forecasting. It examines various model types, input features, forecasting horizons, edge devices, optimization techniques, and practical deployment considerations. The objective is to identify prevailing trends, obstacles, and opportunities within this domain. Ultimately, this research contributes to advancing solar energy forecasting technologies and their practical implementation through the development of efficient and accurate tinyML approaches.