Thermodynamic calculation of partial melting of peridotite using the MELTS algorithm has the potential to aid understanding of a wide range of problems ralated to mantle melting. We review the methodology of MELTS calculations with special emphasis on the features that are relevant for evaluating the suitability of this thermodynamic model for simulations of mantle melting. Comparison of MELTS calculations with well-characterized peridotite partial melting experiments allows detailed evaluation of the strengths and weaknesses of the algorithm for application to peridotite melting problems. Calculaated liquid compositions for partial melting of fertile and depleted peridotite show good agreement with experimental trends for all oxides; for some oxides the agreement between the calculated and experimental concentrations is almost perfect, whereas for others, the trends with melt fraction are comparable, but there is a systematic offset in absolute concentraion. Of particular interest is the prediction oby MELTS that at 1 GPa, near-solidus partial melts of fertile peridotite have markedly higher SiO2 than higher melt fraction liquids, but that at similar melt fractions, calculated partial melts of depleted peridotites re not SiO2 enriched. Similarly, MELTS calculations sugest that near-solidus partial melts of fertile peridotite, but not those of deplted peridotite, have less TiO2 than would be anticipated from higher temperature experiments. Because both experimentw and calculations suggest that these unusual near-solidus melt compositions occur for fertile peridotite but not for depleted peridotite, it is highly unlikely that these effects are the consequence of experimental or model artifacts. Despite these successes of the results of calculations of peridotite melting using MELTS, there are a number of shortcomings to application of this thermodynamic moel to calculations of mantle melting. In particular, calculated compositions of liquids produced by partial melting of peridotite have more MgO and less SiO2 than equivalent experimentally derived liquids. This mismatch, which is caused by overprediction of the stability of orthopyroxene relative to olivine, causes a number of other problems, including calculated temperatures of melting that are too high. Secondarily, the calculated temperatures of melting that are too high. Secondarily, the calculated distribution of Na between pyroxenes and liquid does not match experimentally observed values, which leads to exaggerated calculated Na concentrations for near-solidus partial melts of peridotite. Calculations of small increments of batch melting followed by melt removal predict that fractional melting is less productive than batch melting near the solidus, where the coomposition of the liquid is changing rapidly, but that once the composition of the liquid ceases to change rapidly, fractional and batch melting produce liquid at similar rates per incement of temperature increase until the exhaustion of clinopyroxene. This predicted effect is corroborated by sequential incremental batch melting experiments (Hirose + Kawamura, 1994, Geophysical Research Letters,21, 2139-2142). For melting of peridotite in response to fluxing with water, the calculated effect is that melt fraction increases linearly wit the amount of water added until exhaustion of clinopyroxene (cpx), at which point the proportion of melt created per increment of water added decreases. Between the soslidus and exhaustion of cpx, the amount of melt generated per increment of water added increases with temperature. These trends are similar to those documented experimentally by Hirose + Kawamoto (1995, Earth and Planetary Science Letters,133, 463-473).