This talk concerns the spatial structure of reactive scalar fields in two-dimensional, incompressible chaotic advection flows. Considerations of such fields arise naturally when studying interacting chemical or biological species, such as ozone in the atmosphere and plankton populations in the ocean, where the dominant flow is large-scale and quasi-horizontal. In a regime where diffusion can be neglected (large P´eclet number), the scalar concentration in any fluid parcel is determined by the time history of that parcel. The emerging spatial structures are filamental and characterised by a single scaling regime with a H¨older exponent that depends on the rate of convergence of the reactive processes involved and the stirring induced by the flow, measured by the average rate of divergence of the distance of neighbouring fluid parcels. A theoretical analysis, based on the behaviour of nonlinear ordinary and delay dynamical systems, asymptotic analysis and statistical methods, is developed to understand two distinct problems, both concerned with the scaling behaviour of the spatial structure of the emerging scalar field. The results are confirmed by numerical simulations. The first problem is motivated by models of the evolution of complex organisms such as oceanic zooplankton and considers the effect of introducing a delay time into the reaction term. For sufficiently small scales, all interacting fields share the same spatial structure, as found in the absence of a delay time. For larger scales, depending on the strength of the stirring and the magnitude of the delay time, a second scaling regime, that is unique to the delay system, may appear. The second problem takes into account the inhomogeneous nature of the recent stretching histories of the parcel ensemble in order to improve previous quantitative understanding. The average scaling exponent of the scalar field is modified from previously obtained results with the corrections maximised when the strength of the reactions are comparable to the strength of the flow. The point of transition from a filamental to a smooth field behaviour is re-examined and a new diagnostic for when the transition occurs is developed.