In this paper, we briefly summarize some work on the area of functional spaces in fuzzy analysis and devoted to four directions. The first direction is the development of the fuzzy functional analysis on the setting of topological linear space and several kinds of fuzzy normed linear spaces. Next direction is fuzzy number spaces with different metrics and the embeddings to concrete functional spaces with a linear structure. The third direction is fuzzy continuous function spaces and the approximation by multilayer regular fuzzy neural networks for various fuzzy continuities. The last direction is the space of measurable functions and the space of (Sugeno)integrable functions based on the theory of monotonic measures. In this paper, we also present several suggestions on future research. Wu Congxin was an undergraduate student of the Mathematics Department of Northeastern People's University during 1952-1955, and Professor Hsu guided and supported him so much for long time.