The thermodynamic laws were originally formulated on the basis of global macroscopic cyclic processes in large, which were associated with engines and cycles. However, also the local irreversible processes associated with various flow phenomena in the context of continuum mechanics are believed to be governed by the thermodynamic laws. In this viewpoint, for example, the Navier-- Stokes theory of hydrodynamics can be framed within the constraints of the thermodynamic laws of local flow processes from the viewpoint of irreversible thermodynamics, since it involves linear thermodynamic force--flux relations for the constitutive equations for the stress, heat flux, and so on. Extending this line of approach to the cases of nonlinear thermodynamic force--flux relations, it is possible to formulate a theory of irreversible processes in fluids and thereby frame a generalized theory of hydrodynamics within the constraints of the local forms of the thermodynamic laws. Such a hydrodynamic theory is called generalized hydrodynamics. By starting from the Kelvin--Clausius principle of the second law of thermodynamics, a local theory of hydrodynamic processes will be formulated in such a manner that the thermodynamic laws are satisfied irrespective of the degree of departure from equilibrium. It will be pointed out how the theory formulated phenomenologically can be given kinetic theory foundations by using some kinetic equations known in the literature. Model generalized hydrodynamic equations, which are thermodynamically consistent, will be constructed and applied to study the shock structure of one-dimensional flow in monatomic gases. The theoretical results will be compared with experimental data available in the literature. The possibility of generalizing the theory to molecular gases will be pointed out.