I review some topics in lattice quantum chromodynamics, focusing more on the recent results. These include: (i) the QCD phase diagram in the μ-T plane, (ii) the quark number susceptibilities, and (iii) the screening lengths.

We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for $0.9 \leq T/T_{c} \leq 3$. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.

A critical point in the phase diagram of quantum chromodynamics (QCD), if established either theoretically or experimentally, would be as profound a discovery as the good-old gas–liquid critical point. Unlike the latter, however, first-principles-based approaches are being employed to locate it theoretically. Due to the short-lived nature of the concerned phases, novel experimental techniques are needed to search for it. The Relativistic Heavy Ion Collider (RHIC) in USA has an experimental programme to do so. This short review is an attempt to provide a glimpse of the race between the theorists and the experimentalists as well as the synergy between them.