Modeling of x-ray spectra emitted from a solid-density strongly coupled plasma formed in short-duration, high-power laser-matter interactions represents a highly challenging task due to extreme conditions found in these experiments. In this paper we present recent progress in the modeling and analysis of Kα emission from solid-density laser-produced titanium plasmas. The selfconsistent modeling is based on collisional-radiative calculations that comprise many different processes and effects, such as satellite formation and blending, plasma polarization, Stark broadening, solid-density quantum effects and self-absorption. A rather strong dependence of the Kα shape on the bulk electron temperature is observed. Preliminary analysis of recently obtained experimental data shows a great utility of the calculations, allowing for inferring a temperature distribution of the bulk electrons from a single-shot measurement.