Debris discs are optically thin circumstellar discs that comprise solids in a broad range of sizes, from (sub)micron-sized dust grains up to kilometre-sized planetesimals. The dust component of debris discs is short-lived and continuously replenished through collisional attrition between planetesimals in reservoirs analogous to the Solar system's asteroid and Kuiper belts. Together with planets, debris discs are believed to be the end product of the star and planet formation process. In this thesis, collisional modelling is employed, which simulates the long-term collisional evolution from planetesimals to dust. The calculated dust distributions are used for the comparison with observational data. This powerful technique reveals properties of the underlying dust-producing planetesimal belts which are not directly discernible by observations. The code ACE of the Jena AIU group predicts the evolution of rotationally-symmetric debris discs. ACE calculates collisions between ensembles of circumstellar objects and considers the influence of stellar gravity as well as stellar radiative and corpuscular forces. The code is applied to the systems HIP 17439, AU Mic, and q1 Eri, where the outer part of a debris disc is spatially resolved at multiple wavelengths. All three systems show hints for warm and cold dust populations. The modelling addresses the question of what might be their origin. Two scenarios are considered: a Solar system-like architecture with two planetesimal belts as in-situ sources of dust (Scenario I), and an outer planetesimal belt from which dust is transported inwards by Poynting-Robertson and stellar wind drag (Scenario II). While Scenario I seems to be the most plausible for q1 Eri, Scenario II is preferred for AU Mic. However, no strict conclusion can be drawn for HIP 17439, where both scenarios are possible. More than two planetesimal belts or even a radially extended planetesimal belt cannot be excluded either.