Recent advances in deep learning have made learning representation from ever-growing datasets possible in the domain of vision, natural language processing (NLP), and robotics, among others. However, deep networks are notoriously data-hungry; for example, training language models with attention mechanisms sometimes requires trillions of parameters and tokens. In contrast, we can often access a limited number of samples in many tasks. It is crucial to learn models from these `limited' datasets. Learning with limited datasets can take several forms. In this thesis, we study how to select data samples sequentially such that downstream task performance is maximized. Moreover, we study how to introduce prior knowledge in the deep networks to maximize prediction performance. We focus on four sequential tasks: computerized adaptive testing in psychometrics, sketching in recommender systems, knowledge tracing in computer-assisted education, and career path modeling in the labor market. In the first two tasks, we devise novel sample-efficient algorithms to query a minimal number of sequential samples to improve future predictions. We propose a Bilevel Optimization-Based framework for computerized adaptive testing to learn a data-driven question selection algorithm that improves existing data selection policies. We also tackle the sketching problem in the recommender system, with the task of recommending the next item using a stored subset of prior data samples. In this setting, we develop a data-driven sequential selection algorithm that tackles evolving downstream task distribution. In the last two tasks, we devise novel neural models to introduce prior knowledge exploiting limited data samples. For knowledge tracing, we propose a novel neural architecture, inspired by cognitive and psychometric models, to improve the prediction of students' future performance and utilize the labeled data samples efficiently. For career path modeling, we propose a novel and interpretable monotonic nonlinear state-space model to analyze online user professional profiles and provide actionable feedback and recommendations to users on how they can reach their career goals. The data-driven differentiable data selection algorithms for the first two tasks open up future directions to query (a non-differentiable operation) a minimal number of samples optimally to maximize prediction performance. The structures, introduced in the neural architecture for the models in the last two tasks using prior knowledge, open up future directions to learn deep models augmented with prior knowledge using limited data samples.