The study of lattice knots in the cubic lattice started in 1988 when the Frisch-Wasserman-Delbruck conjecture was proven by Sumners and Whittington (J Phys A Math Gen 21: L857–861, 1988), and also by Pippenger (Disc Appl Math 25: 273–278, 1989). In this talk I will review this model and its applications, and in particular focus on the numerical sampling techniques used to simulate lattice knots. These include the use of BFACF moves implemented in Metropolis style MC algorithms, or implemented in dynamic growth algorithms such as GAS to approximately enumerate lattice knots. I will discuss some long standing open problems in this model, and also present some results about the physical properties of lattice knots in confined spaces.