Contents

1. Introduction

2. Dynamical percolation: first results

3. Exceptional times of percolation: the tree case

4. Noise sensitivity, noise stability, influence and the Fourier spectrum

5. Critical exponents for percolation

6. Exceptional times and positivity of the noise sensitivity exponent for the hexagonal lattice

7. The exact Hausdorff dimension of exceptional times and the exact noise sensitivity exponent for the hexagonal lattice

8. Sensitivity of the infinite cluster in critical percolation

9. Dynamical percolation and the incipient infinite cluster

10. The scaling limit of planar dynamical percolation

11. Dynamical percolation for interacting particle systems