In this work we present Monte Carlo simulations of particle and polymer diffusion in tworndimensional (2D) media with obstacles distributed randomly. For diffusion of a particle,rnthe mean-square displacement of the diffusing species is proportional to time for normalrndiffusion. But in disordered systems anomalous diffusion may occur, in which the meansquarerndisplacement is proportional to some other power of time. In the presence ofrnmoderate concentration of obstacles, diffusion is anomalous for short times and normalrnfor long times. Monte Carlo calculations are used to characterize anomalous diffusionrnfor obstacle concentrations between zero and the percolation threshold. As the obstaclernconcentration approaches the percolation threshold, diffusion becomes more anomalousrnfor long times; the anomalous diffusion exponent increases. In polymer diffusion, wernpresent a new effective algorithm to simulate dynamic properties of polymeric systemsrnconfined to lattice. The algorithm displays Rouse behavior for all spatial dimensions. Thernsystems are simulated by bond fluctuation method to study both the static and dynamicrnproperties of the polymer chains. For static properties we calculated the average meansquarernend-to-end distance hR2(N)i and the mean-square radius of gyration hR2rng(N)i.rnBoth the end-to-end distance and the radius of gyration are proportional to some powerrnof the number of monomers (N), hR2(N)i _ N3/2 and hR2rng(N)i _ N3/2. For dynamicalrnproperties we look at the mean-square displacement of the total chain. For short timesrnthe mean-square displacement of the monomers g1(t) and the mean-square displacementrnof the monomers relative to the chains center of mass g2(t) show the same behavior andrnfor long times the mean-square displacement of the center of mass g3(t) takes over