Unit continuous probability distributions play a fundamental role in modeling variables bounded within the interval $[0,1]$, such as proportions and probabilities. In recent decades, there has been a significant increase in the development of new parametric families of these distributions. In this work, we present a comprehensive and up-to-date review of more than one hundred unit continuous distributions, including classical models, such as the beta and Kumaraswamy distributions, along with their various extensions. We examined key statistical properties such as moments and demonstrated the practical effectiveness of twelve selected distributions through applications to nine distinct datasets, thereby highlighting their flexibility in modeling a wide range of data types. To the best of our knowledge, this is the most extensive review focused specifically on unit distributions and is a valuable reference for researchers and practitioners.