This chapter describes the calculation of heat kernel coefficients for Laplace-like operators on smooth manifolds with smooth boundaries and various boundary conditions. The main emphasis is on the determination of the boundary contribution to the heat kernel coefficients. The chapter provides the general form of the heat kernel coefficients for Dirichlet and Robin boundary conditions. It discusses heat equation asymptotics for these boundary conditions and summarizes the result. The chapter derives the heat kernel coefficients for spectral boundary conditions and provides some recently obtained results on time-dependent boundary conditions, transmittal boundary conditions and on the so-called Zaremba problem. It also discusses the spectral problem, where the field satisfies Dirichlet conditions on one part of the boundary of the relevant domain and Neumann (or Robin) on the remainder.