QCD thermodynamics at zero and non-zero density

We present recent results on thermodynamics of QCD with almost physical light quark masses and a physical strange quark mass value. These calculations have been performed with an improved staggerd action especially designed for finite temperature lattice QCD. In detail we present a calculation of the transition temperature, using a combined chiral and continuum extrapolation. Furthermore we present preliminary results on the interaction measure and energy density at almost realistic quark masses. Finally we disscuss the response of the pressure to a finite quark chemical potential. Within the Taylor expansion formalism we calculate quark number susceptibilities and leading order corrections to finite chemical potential. This is particularly usefull for mapping out the critical region in the QCD phase diagram.