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This talk will describe a general recipe for replacing discrete stochastic processes by deterministic analogues that satisfy the same first-order limit laws but have smaller fluctuations. The recipe will be applied to several illustrative problems in the study of random walk and random aggregation. In particular, a derandomized version of the internal diffusion-limited aggregation model in two dimensions gives rise to a growing blob that is remarkably close to circular and also displays intriguing internal structures (see http://www.math.wisc.edu/~propp/million.gif). This is joint work with Ander Holroyd and Lionel Levine. An early write-up of derandomized aggregation: www.math.wisc.edu/~propp/hidden/rotor Email-log of some messages I sent out about derandomized walk: www.math.wisc.edu/~propp/hidden/test/rotorwalk.to Lionel Levine's undergraduate thesis: www.math.berkeley.edu/~levine/rotorrouter.pdf Slides from a talk given by Lionel Levine: www.math.berkeley.edu/~levine/slides/ Lionel Levine and Adam Kampff's picture of the rotor-router aggregation blob after 270,000 particles have aggregated: www.math.berkeley.edu/~levine/private/rotorrouter/bigblob.bmp Two close-ups of that same picture: www.math.berkeley.edu/~levine/private/rotorrouter/closeup.bmp Ed Pegg's picture of the rotor-router blob after 750,000 particles have aggregated: www.math.wisc.edu/~propp/proppcircle.gif Ander Holroyd's picture of the rotor-router blob after 1,000,000 particles have aggregated: www.math.wisc.edu/~propp/million.gif Vishal Sanwalani's picture of the state achieved by the abelian sandpile model when sixty thousand grains have been added: www.math.wisc.edu/~propp/hidden/501.gif Hal Canary's applets for demonstrating derandomized walk and aggregation: http://ups.physics.wisc.edu/~hal/SSL/2003/ ©2003 Microsoft Corporation. All rights reserved.