Algorithm design methods for radio communications systems are poised to undergo a massive disruption over the next several years. Today, such algorithms are typically designed manually using compact analytic problem models. However, they are shifting increasingly to machine learning based methods using approximate models with high degrees of freedom, jointly optimized over multiple subsystems, and using real-world data to drive design which may have no simple compact probabilistic analytic form. Over the past five years, this change has already begun occurring at a rapid pace in several fields. Computer vision tasks led deep learning, demonstrating that low level features and entire end-to-end systems could be learned directly from complex imagery datasets, when a powerful collection of optimization methods, regularization methods, architecture strategies, and efficient implementations were used to train large models with high degrees of freedom. Within this work, we demonstrate that this same class of end-to-end deep neural network based learning can be adapted effectively for physical layer radio systems in order to optimize for sensing, estimation, and waveform synthesis systems to achieve state of the art levels of performance in numerous applications. First, we discuss the background and fundamental tools used, then discuss effective strategies and approaches to model design and optimization. Finally, we explore a series of applications across estimation, sensing, and waveform synthesis where we apply this approach to reformulate classical problems and illustrate the value and impact this approach can have on several key radio algorithm design problems. / Ph. D.