Cloud computing and network slicing are essential concepts of forthcoming 5G mobile systems. Network slices are essentially chunks of virtual computing and connectivity resources, configured and provisioned for particular services according to their characteristics and requirements. The success of cloud computing and network slicing hinges on the efficient allocation of virtual resources (e.g., VCPU and VMDISK) and the optimal placement of virtualized network functions (VNFs) composing the network slices. In this context, this paper elaborates issues that may disrupt the placement of VNFs and virtual machines (VMs). This paper classifies the existing solutions for VM placement based on their nature, whether the placement is dynamic or static, their objectives, and their metrics. This paper then proposes a classification of VNF placement approaches, first, regarding the general placement and management issues of VNFs, and second, based on the target VNF type.