The design of wireless communication receivers to enhance signal processing in complex and dynamic environments is going through a transformation by leveraging deep neural networks (DNNs). Traditional wireless receivers depend on mathematical models and algorithms, which do not have the ability to adapt or learn from data. In contrast, deep learning-based receivers are more suitable for modern wireless communication systems because they can learn from data and adapt accordingly. This survey explores various deep learning architectures such as multilayer perceptrons (MLPs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), generative adversarial networks (GANs), and autoencoders, focusing on their application in the design of wireless receivers. Key modules of a receiver such as synchronization, channel estimation, equalization, space-time decoding, demodulation, decoding, interference cancellation, and modulation classification are discussed in the context of advanced wireless technologies like orthogonal frequency division multiplexing (OFDM), multiple input multiple output (MIMO), semantic communication, task-oriented communication, and next-generation (Next-G) networks. The survey not only emphasizes the potential of deep learning-based receivers in future wireless communication but also investigates different challenges of deep learning-based receivers, such as data availability, security and privacy concerns, model interpretability, computational complexity, and integration with legacy systems.