In this paper, we review a variety of deep learning algorithms and models for modulation recognition and classification of wireless communication signals. Specifically, deep learning (DL) has shown overwhelming advantages in computer vision, robotics, and voice recognition. Recently, DL has been proposed to apply to wireless communications for signal detection and classification in order to better learn the active users for electromagnetic spectrum sharing purposes. Therefore, we aim to provide a survey on the most recent techniques which use DL for recognizing and classifying a wireless signal. We focus on the most widely used DL models, emphasize the advantages and limitations, and discuss the challenges as well as future directions. In addition, we also apply a DL algorithm, convolutional neural network (CNN), to demonstrate the feasibility of using CNN to recognize and classify the over-the-air wireless signals using Mathworks DL toolbox with PlutoSDR and Universal Software Radio Peripheral (USRP), respectively.