We address the long-standing puzzle of why some proteins find their targets faster than allowed by 3D diffusion. To this end, we measured the onedimensional diffusion of LacI repressor proteins along elongated Lambda DNA using single molecule imaging techniques. We find that (1) LacI diffuses along nonspecific sequences of DNA in the form of 1D Brownian motion; (2) the observed 1D diffusion coefficients DDNA vary over an unexpectedly large range, from 2.3 × 10-12 cm2/s to 1.3 × 10-9 cm2/s; (3) the lengths of DNA covered by these 1D diffusions vary from 120nm to 2920 nm; and (4) the mean values of D DNA and the diffusional lengths indeed predict a LacI target binding rate 90 times faster than the 3D diffusion limit. The first half of this chapter is a tutorial on the models we use to think about the physics, the limited and noisy data, and how to squeeze the maximum amount of physics from these data. The second half is about our experiments and results.