The talk consists of two parts. Its rst part is devoted to Monte Carlo (DSMC) methods. The general DSMC method for solving Boltzmann equation for long-range potentials and Landau-Fokker-Planck equation was proposed by Bobylev and Nanbu in 2000 [1] (partly as a development of earlier appoach of Nanbu [2] to Coulomb collisions). The methods of [1], [2] were later applied to various model problems of plasma physics, discussed in detail and further developed by several authors (see, for example, [3], [4] and references in [4]). However the general method of [1] was not clearly understood and therefore many authors still use a more complicated original scheme of [2] with reference to [1] just for the formal proof of consistency with the Landau-Fokker-Planck equation. The reason is that the rst presentation of the method was done in [1] in too formal and general way. We present in this talk a completely di erent approach, which leads to basically the same general method, but makes its essence absolutely clear and transparent. The method is explained for the general case of multi-component plasma. We also present some rigorous estimates for accuracy of the method. Finally some numerical results on typical problems of physics of collisional plasma are presented and discussed. The details of the rst part of the talk can be found in the recently published paper [5]. The second part of the talk is devoted to a brief discussion of some open mathematical problems for the Landau equation. In particular, these are problems related to (a) consistency of this equation with dynamics, (b) existence of the global in time solution for the spatially homogeneous case, and (c) some asymptotic problems. It is important to stress that the discussion is related to the true Landau equation which formally corresponds to the Coulomb potential. This is because all other forms of the Landau equation (as a formal limit of the Boltzmann equation for grazing collisions) are not directly connected with physics. On the other hand, the true Landau equation is connected not only with physical systems of charged particles, but also with particles interacting via any bounded smooth potential in the weak coupling limit. References [1] A.V. Bobylev and K.Nanbu, Theory of collision algorithms for gases and plas- mas based on the Boltzmann equation and the Landau-Fokker-Planck equation , Phys.Rev. E 61 (2000) [2] K. Nanbu, Theory of cumulative small-angle collisions in plasmas , Phys.Rev. E 55 (1997) [3] A.V. Bobylev, E. Mossberg and I.F. Potapenko, A DSMC method for the Landau- Fokker-Planck equation , in the book Rare ed Gas Dynamics (Proc. of 25th RGD Symposium, St. Petersburg, July 2006), Eds. M.S.Ivanov and A.K.Rebrov, 479{ 483, Novosibirsk (2007). [4] G. Dimarco, R .Ca isch, L. Pareschi Direct Simulation Monte Carlo schemes for Coulomb interactions in plasmas , Commun. Appl. Indust. Math. 1 (2010) [5] A.V. Bobylev, I.F.Potapenko, Monte Carlo methods and their analysis for Coulomb collisions in multicomponent plasmas, J. Comput. Phys. 246(2013)