The Planck satellite has confirmed cosmological inflation as the most successful paradigm for the generation of primordial fluctuations. It is important to understand what the data is exactly telling us concerning the dynamics of inflation. This colloquium will describe an analysis of randomly generated models of inflation, motivated by the complex multi-field potential shapes that might be generated by the string landscape. Both canonical scalar field models and brane-motivated models are studied. The main observables (spectral tilt, tensor-to-scalar ratio, and primordial non-gaussianity) are computed and compared with observations.