Highly relevant for both clinical and legal medicine applications, the established radiological methods for estimating unknown age in children and adolescents are based on visual examination of bone ossification in X-ray images of the hand. Our group has initiated the development of fully automatic age estimation methods from 3D MRI scans of the hand, in order to simultaneously overcome the problems of the radiological methods including (1) exposure to ionizing radiation, (2) necessity to define new, MRI specific staging systems, and (3) subjective influence of the examiner. The present work provides a theoretical background for understanding the nonlinear regression problem of biological age estimation and chronological age approximation. Based on this theoretical background, we comprehensively evaluate machine learning methods (random forests, deep convolutional neural networks) with different simplifications of the image information used as an input for learning. Trained on a large dataset of 328 MR images, we compare the performance of the different input strategies and demonstrate unprecedented results. For estimating biological age, we obtain a mean absolute error of 0.37 ± 0.51 years for the age range of the subjects ≤ 18 years, i.e. where bone ossification has not yet saturated. Finally, we validate our findings by adapting our best performing method to 2D images and applying it to a publicly available dataset of X-ray images, showing that we are in line with the state-of-the-art automatic methods for this task.