This paper provides an overview of variants and extensions of the resource-constrained project scheduling problem (RCPSP). The RCPSP is a well-known problem in project scheduling, where activities must be scheduled subject to precedence and resource constraints to minimize the makespan. However, the basic RCPSP has restrictive assumptions that are not suitable for many practical applications. Therefore, various extensions of the RCPSP have been developed. The paper classifies these extensions according to the structure of the RCPSP and summarizes generalizations of the activity concept, precedence relations, and resource constraints. It also discusses alternative objectives and approaches for scheduling multiple projects. In addition to popular variants such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper provides a survey of many less known concepts. The paper also discusses various extensions of the RCPSP, including preemptive scheduling, resource requests varying with time, setup times, multiple modes, tradeoff problems, generalized temporal constraints, release dates and deadlines, time-switch constraints, further temporal constraints, logical dependencies, and network representations. The paper also discusses generalized resource constraints, including nonrenewable and doubly constrained resources, partially renewable resources, cumulative resources, continuous resources, dedicated resources, and resource capacities varying with time. Finally, the paper discusses alternative objectives, including time-based objectives, robustness-based objectives, and objectives for rescheduling.This paper provides an overview of variants and extensions of the resource-constrained project scheduling problem (RCPSP). The RCPSP is a well-known problem in project scheduling, where activities must be scheduled subject to precedence and resource constraints to minimize the makespan. However, the basic RCPSP has restrictive assumptions that are not suitable for many practical applications. Therefore, various extensions of the RCPSP have been developed. The paper classifies these extensions according to the structure of the RCPSP and summarizes generalizations of the activity concept, precedence relations, and resource constraints. It also discusses alternative objectives and approaches for scheduling multiple projects. In addition to popular variants such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper provides a survey of many less known concepts. The paper also discusses various extensions of the RCPSP, including preemptive scheduling, resource requests varying with time, setup times, multiple modes, tradeoff problems, generalized temporal constraints, release dates and deadlines, time-switch constraints, further temporal constraints, logical dependencies, and network representations. The paper also discusses generalized resource constraints, including nonrenewable and doubly constrained resources, partially renewable resources, cumulative resources, continuous resources, dedicated resources, and resource capacities varying with time. Finally, the paper discusses alternative objectives, including time-based objectives, robustness-based objectives, and objectives for rescheduling.