The resource allocation problem seeks to find an optimal allocation of a fixed amount of resources to activities so as to minimize the cost incurred by the allocation. The simplest form of the problem is to minimize a separable convex function under a single constraint concerning the total amount of resource to be allocated. The amount of resource to be allocated to each activity is treated as a continuous or integer variable, depending on the situations. Hence, this problem can be viewed as a special case of the nonlinear optimization problem or the nonlinear integer optimization problem. Due to its simple structure, the resource allocation problem is encountered in a variety of application areas, including load distribution, production planning, computer resource allocation, queueing control, portfolio selection, and apportionment. The first explicit investigation of the resource allocation problem was due to a paper by Koopman [90], published in 1953, where he discussed optimal distribution of efforts that arises from the problem of searching for an object whose position is a random variable. Since then, a great number of papers on the resource allocation problem have been published. Efficient algorithms have also been developed, depending on the types of objective functions, constraints, and variables (i.e., continuous or integer). In 1988, two of the present authors, Ibaraki and Katoh, have published a book [69] that gave a comprehensive review of the state of the art of the resource allocation problem. Since then, more than 30 years have passed, during which many papers on this problem have been published. A significant progress has been made on the algorithm side. Also, new generalizations and variants of the problem have been investigated, and new application fields have been discovered. The main purpose of this chapter is to give a brief overview of the recent progress on the theory and applications, putting emphasis on cases with integer variables.