The DLA process is known as a model for numerous physical phenomena including the growth of the snowflakes, viscous fingering, and the dielectric breakdown. The process appears to be quite intractable mathematically, and therefore the study of some simpler growth models depending on the distribution of harmonic measure and isolating certain features of the DLA has received considerable attention. In my talk, I will review some recent results on such growth models. In particular, I will discuss the non-branching DLA process, Hele-Shaw equations, and random Loewner chains.