## 7 Conclusions  
We have given a review on the recent progress in the development of low temperature detectors with a large array of TES-based microcalorimeters for application in astro-particle physics. While X-ray TES microcalorimeters have already demonstrated an exquisite resolving power in the energy band from \(0.2\) to \(10\) keV, we believe a continuous optimization of the detector design and its read-out is required to achieve the ultimate performance in the complex instruments discussed here. A further improvement in the TES design might lead to the demonstration of energy resolution better than 1.5 eV at 6 keV and below 1 eV at lower energies, within the existing X-ray microcalorimeters fabrication technology. For this reason, we have placed emphasis on the underlying detector physics and the deep interaction between the detectors properties and the multiplexing configuration. Researchers are striving to achieve a realistic description of the complex physical phenomena observed at the superconducting transition of TESs with extended geometry and complex structures, including the current leads and the coupled normal metal absorber. We have given the reader an overview of the most recent models developed to predict the TES resistive transition and the noise. Those models can be implemented in the generalized system of coupled differential equations for a TES and its read-out circuit. The equations can be solved numerically to calculate the detector large signal response and realistically predict the dynamic interaction with the read-out circuit. This approach can be used as a building block for a detector simulator. Thanks to the available computational power of modern computers, the simulation of complex instruments with a large amount of pixels distributed on many read-out channels will give the researchers and engineers a powerful tool to guide the detector development and the instrument calibration. The energy resolution of multiplexed pixels arrays is approaching the best results observed in single pixel configuration. Driven by the development of the X-IFU instrument of the ESA future large space mission Athena, the research field of TES X-ray microcalorimeters is entering a very interesting phase with the focus on demonstrating, in the next decade, the performance of a full instrument with more than thousand pixels. The progress booked by the community over the past 12 years is summarized in Figure 14. We show, for each multiplexing technology and for X-ray photons with 5.9 keV energy, the improvement over the years on the multiplexed energy resolution, the multiplexing factor per channel, the multiplexing factor per channel normalized to the energy resolution, and the total number of pixels read-out simultaneously in multi-channels experiments. Both the energy resolution and the multiplexing factor for the time division and the MHz-frequency division multiplexing are not expected to improve dramatically in the next year, being limited by fundamental noise sources in the TES and by the detector and read-out bandwidth ratio. On the contrary, the total number of pixels depends on the total number of read-out channels that an instrument can host. It will likely increase by about a factor of two every two years in the next decade, with the ultimate demonstration provided by the XIFU flight model, which is expected to be tested on ground in 2029. A lot of efforts have to be devoted in the coming years to improve even further the efficiency of the multiplexing read-out techniques to achieve the ambitious goal of building future instruments with 100,000-pixels array beyond 2030. **Author Contributions:** Conceptualization, writing and editing, [PERSON]; [PERSON] took care of the conceptualization and writing of the section on the detector fabrication. All authors have read and agreed to the published version of the manuscript. **Funding:** This work is partly funded by European Space Agency (ESA) under ESA CTP contract ITT AO/1-7947/14/NL/BW and ESA CTP Contract No.