Managing invasive species is inherently a spatial problem, even though the application of management is local. For efficient management of invasive species, we must therefore understand their spatial population dynamics. Once key demographic and dispersal rates are studied in detail, spatial population models can be constructed and utilized to evaluate the impact of various management options. We illustrate this approach for the invasive thistles Carduus acanthoides and Carduus nutans in North America, where these Eurasian plants arrived in the 19 th century. The invasion routes through North America were reconstructed from a literature review: within 150 years both species have reached most US states and Canadian provinces. At the continental scale, these high invasion rates are most likely caused by human transport. However, within states the distributions are patchy. At this regional/local scale, wind dispersal of the plumed seeds is also important. Therefore, at the scale of neighboring farms, management can be informed by mechanistic population models that incorporate both wind and human dispersal. One of the foundations of a spatial population model is the local dynamics of a species. By revisiting known populations three years later, we show that initial size of C. nutans populations has a strong impact on the persistence and growth of these populations. More than fifty percent of small populations went extinct in those three years, whereas larger populations had higher persistence rates. This can be attributed to demographic stochasticity, but experimental results suggest that this can also be partly explained by reduced pollinator services in small thistle populations. Local population dynamics can be studied in more detail by following the fate of individuals and by relating the performance of individuals to their size. The resulting size-structured population models have indeed proven to be useful for studying thistle populations. Another key component of spatial population models is dispersal. We have been studying all key aspects of the dispersal process in these Carduus thistles: seed release, movement, and impact upon arrival. The seed release phase has been mainly studied in wind tunnel experiments which show that it is possible to predict the timing of seed release based on flowering phenology and weather data. Furthermore, field experiments on seed dispersal have shown that the resulting probability density kernel of dispersal distances can be well fitted by a semi-mechanistic WALD model. This allows us to simulate realistic dispersal kernels based on wind speed, turbulence, release and vegetation height, and seed terminal velocity. Now these demography and dispersal components of the spatial population dynamics need to be integrated. We have started doing so with spatially-implicit matrix and integral projection models. We expect that the field of invasion ecology will move towards more process-oriented, transparent, analytical models with increasing biological realism. Alternatively the same demography and dispersal functions can be used in spatially-explicit population models that trade tractability for the flexibility to also include the effects of heterogeneous landscape configurations and species interactions on both local population dynamics and seed dispersal.