In this thesis we study the long-range percolation model on Z^d, where each pair of vertices x, y ∈  Z^d form a connection with probability 1 − exp(−βJ(x, y)), and J(x, y) decays asymptotically with the form ∥x − y∥^−dα. The parameter α > 0 is fixed, while β can be varied. This model is an extension of the classical Bernoulli bond percolation model allowing the modeling of connection phenomena where long-distance connections play a crucial role. In this paper we study the critical value β_c, the percolation probability θ(β) = P_β (|K₀| = ∞) and we investigate the critical exponent δ explaining the cluster decay at criticality. We compile known bounds for the critical exponent δ and derive foundational results for β_c. In the numerical part we simulate long-range percolation on finite boxes, create new estimators for the percolation probability θ(β) and studying existing ones for the critical parameter β_c. Using this estimate for β_c we estimate the critical parameter δ using linear regression. The estimators for θ(β) and β_c show consistent stable behaviour conforming to theory. The estimates for δ in contrast are sensitive to the finite size approximation, showcasing the limits of simulating critical parameters on a finite scale. ... Read more