Despite decades of research, our understanding of functional brain development throughout childhood and adolescence remains limited due to the challenges posed by certain neuroimaging modalities. Recently, there has been a growing interest in using functional near-infrared spectroscopy (fNIRS) to elucidate the neural basis of cognitive and socioemotional development and identify the factors shaping these types of development. This article, focusing on the fNIRS methods, presents an up-to-date systematic review of fNIRS studies addressing the effects of age and other factors on brain functions in children and adolescents. Literature searches were conducted using PubMed and PsycINFO. A total of 79 fNIRS studies involving healthy individuals aged 3–17 years that were published in peer-reviewed journals in English before July 2020 were included. Six methodological aspects of these studies were evaluated, including the research design, experimental paradigm, fNIRS measurement, data preprocessing, statistical analysis, and result presentation. The risk of bias, such as selective outcome reporting, was assessed throughout the review. A qualitative synthesis of study findings in terms of the factor effects on changes in oxyhemoglobin concentration was also performed. This unregistered review highlights the strengths and limitations of the existing literature and suggests directions for future research to facilitate the improved use of fNIRS in developmental cognitive neuroscience research.