Abstract: Consider Bernoulli first-passage percolation on the triangular lattice in which sites have 
and 
passage times with probability 
and 
, respectively. First, I will discuss a result in the subcritical regime, which is based on https://arxiv.org/abs/2104.01211. Let 
denote the correlation length, and let 
denote the limit shape in the classical shape theorem. I will show that the re-scaled limit shape 
converges to a Euclidean disk, as tends to 
from below. The proof relies on the scaling limit of near-critical percolation established by Garban, Pete and Schramm (2018) and the construction of the collection of continuum clusters introduced by Camia, Conijn and Kiss (2019). Next, I will review some recent results and problems in the critical and supercritical cases.