The study of the dynamics of growing interfaces is a topic of multidisciplinary research that is relevant in many fields such as physics, chemistry, biology, catalysis, ecology, etc. After a brief overview of key concepts such as dynamic scaling of self-affine interfaces and the discussion of continuous equations for the evolution of growing interfaces, this article addresses the competitive dynamics of growing interfaces. Two competitive mechanisms are discussed: on the one hand the interface is generated by two competitive mechanisms and, on the other hand the interface results from the collision of two growing interfaces.

The occurrence of the competing mechanisms can be rationalized by means of a generalized dynamic scaling relationship. Also, a mesoscopic (continuous) equation for the description of this process is formulated and discussed.

It is shown that for the case of colliding interfaces, the asymptotic time regime is dominated by the mechanisms that make the resulting interface rougher. The relevance of the studied processes for various experimental situations such as collision of chemical waves, deposition of alloys, collision of fire fronts, competitive growth of biological species, etc., is also discussed.