In the last two decades, the asteroid research has been significantly influenced by theoretical results obtained in the field of applied mathematics. The first step was the so called "lightcurve inversion", which is an inversion method that reconstructs a shape of an asteroid from its disk-integrated photometry. With this method, almost one thousand asteroid models have been derived so far. Its potential is much larger - it will enable us to reconstruct shapes and spin states of a significant fraction of the whole asteroid population. Together with photometry, other disk-resolved (low-resolution images, silhouettes from occultations,...) or disk-integrated data (thermal infrared flux, for example) can be analyzed and detailed models can be derived by so called "multi-modal data inversion". In this talk, I will (i) review lightcurve inversion method, (ii) highlight the main achievements accomplished in the asteroid research with lightcurve inversion, (iii) describe the role of disk-resolved data, and (iv) mention the plans and prospects for the future, in particular the cooperation within the KMTNet and LSST projects.