This article surveys convolution-based models including convolutional neural networks (CNNs), Conformers, ResNets, and CRNNs-as speech signal processing models and provide their statistical backgrounds and speech recognition, speaker identification, emotion recognition, and speech enhancement applications. Through comparative training cost assessment, model size, accuracy and speed assessment, we compare the strengths and weaknesses of each model, identify potential errors and propose avenues for further research, emphasizing the central role it plays in advancing applications of speech technologies.