This dissertation presents several novel deep-learning (DL)-based approaches for classifying digitally modulated signals, one method of which involves the use of capsule networks (CAPs) together with cyclic cumulant (CC) features of the signals. These were blindly estimated using cyclostationary signal processing (CSP) and were then input into the CAP for training and classification. The results showed that the classification of digitally modulated signals using CAPs and CCs proposed in this dissertation outperformed alternative approaches for classifying digitally modulated signals that included conventional classifiers that employed CSP-based techniques, as well as alternative DL-based classifiers that used various conventional neural networks (NNs) with in-phase/quadrature (I/Q) data used for training and classification. Another method of digital modulation classification presented in this dissertation showcases two novel DL-based classifiers that each use a CAP with custom-designed feature extraction layers. The classifiers take I/Q data as input, and the feature extraction layers are inspired by CSP techniques, which extract the CC features employed by conventional CSP-based approaches to blind modulation classification and signal identification. Specifically, the feature extraction layers implement a proxy of the mathematical functions used in the calculation of the CC features and include a squaring layer, a raise-to-the-power-of-three layer, and a fast-Fourier-transform (FFT) layer, along with additional normalization and warping layers to ensure that the relative signal powers are retained and to prevent the trainable NN layers from diverging in the training process.