Seismic inversion is a fundamental tool in geophysical analysis, providing a window into the Earth. In particular, it enables the reconstruction of large scale subsurface earth models for hydrocarbon exploration, mining, earthquakes analysis, shallow hazard assessment and other geophysical tasks. This article provides a comprehensive and timely overview of emerging datadriven Deep Learning (DL) solutions to seismic inverse problems, including velocity, impedance, reflectivity model building and seismic bandwidth extension. The article reviews seismic wave propagation and signal acquisition principles using large scale sensor arrays in offshore and inland exploration. In addition, the relations between the seismic forward and inverse problems are established, and prominent model-based solutions including seismic tomography, Full-Waveform Inversion (FWI) and multiscale FWI are explained. A primer to DL principles is presented, including empirical risk minimization, stochastic gradient-based learning, Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN) and regularization. The article then presents DL-based solutions addressing full seismic inversion as well as DL-assisted FWI solutions including Encoder-Decoder architectures, CNN-based networks and RNN-based networks with Long Short Term Memory and Gated Recurrent Units. Seismic signals features extraction methods such as semblance velocity analysis and seismic spectrograms are discussed, as well as batch vs. sequential data processing architectures. The article further presents advanced solutions based on Generative Adversarial Networks , and Physics-guided DL architectures that incorporate numerical geophysical modeling into the DL training loop, enabling unsupervised and semi-supervised learning.