Naturalistic recordings capture audio in real-world environments where participants behave naturally without interference from researchers or experimental protocols. Naturalistic long-form recordings extend this concept by capturing spontaneous and continuous interactions over extended periods, often spanning hours or even days, in participants' daily lives. Naturalistic recordings have been extensively used to study children's behaviors, including how they interact with others in their environment, in the fields of psychology, education, cognitive science, and clinical research. These recordings provide an unobtrusive way to observe children in real-world settings beyond controlled and constrained experimental environments. Advancements in speech technology and machine learning have provided an initial step for researchers to automatically and systematically analyze large-scale naturalistic recordings of children. Despite the imperfect accuracy of machine learning models, these tools still offer valuable opportunities to uncover important insights into children's cognitive and social development. Several critical speech technologies involved include speaker diarization, vocalization classification, word count estimate from adults, speaker verification, and language diarization for code-switching. Most of these technologies have been primarily developed for adults, and speech technologies applied to children specifically are still vastly under-explored. To fill this gap, we discuss current progress, challenges, and opportunities in advancing these technologies to analyze naturalistic recordings of children during early development (<3 years of age). We strive to inspire the signal processing community and foster interdisciplinary collaborations to further develop this emerging technology and address its unique challenges and opportunities.