Ultralow-noise microwave amplification and detection play a central role in different applications, going from fundamental physics experiments to the deployment of quantum technologies. In many applications the necessity of reading multiple detectors, or cavities or qubits, calls for large bandwidth amplifiers with the lowest possible noise. Current technologies are based on High Electron Mobility Transistors and Josephson Parametric Amplifiers. Both have limitations, the former in terms of the minimum noise, the latter in terms of bandwidth. Superconducting Traveling Wave Parametric Amplifiers (TWPAs) have the potential of offering quantum limited noise and large bandwidth. These amplifiers are based on the parametric amplification of microwaves traveling along a transmission line with embedded nonlinear elements. We are developing superconducting TWPAs based both on Josephson junction arrays (Traveling Wave Josephson Parametric Amplifiers) and on nonlinear kinetic inductance (Dispersion Engineered Traveling Wave Kinetic Inductance Amplifiers). Our goal is to achieve large bandwidth (in the 5 to 10 GHz range), large gain (more than 20 dB), large saturation power (more than -50 dBm), and near quantum limited noise (noise temperature less than 600 mK). Current achievements in the design and development of the high performance TWPAs are here reported and discussed, together with current limitations and possible future developments.