Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F. -Y. Wang [Ann. Probab., 2012, 42(3): 994-1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with nonLipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established.Keywords Shift Harnack inequality, integration by parts formula, stochastic partial differential equation (SPDE), stochastic functional partial differential equation (SFPDE), path space, log-Sobolev inequality MSC 60H15