Acoustic echo cancellation (AEC), noise suppression (NS) and dereverberation (DR) are an integral part of modern full-duplex communication systems. As the demand for teleconferencing systems increases, addressing these tasks is required for an effective and efficient online meeting experience. Most prior research proposes solutions for these tasks separately, combining them with digital signal processing (DSP) based components, resulting in complex pipelines that are often impractical to deploy in real-world applications. This paper proposes a real-time cross-attention deep model, named DeepVQE, based on residual convolutional neural networks (CNNs) and recurrent neural networks (RNNs) to simultaneously address AEC, NS, and DR. We conduct several ablation studies to analyze the contributions of different components of our model to the overall performance. DeepVQE achieves state-of-the-art performance on non-personalized tracks from the ICASSP 2023 Acoustic Echo Cancellation Challenge and ICASSP 2023 Deep Noise Suppression Challenge test sets, showing that a single model can handle multiple tasks with excellent performance. Moreover, the model runs in real-time and has been successfully tested for the Microsoft Teams platform.