NFV is an emerging network architecture to increase flexibility and agility within operator's networks by placing virtualized services on demand in Cloud data centers (CDCs). One of the main challenges for the NFV environment is how to efficiently allocate Virtual Network Functions (VNFs) to Virtual Machines (VMs) and how to minimize network latency in the rapidly changing network environments. Although a significant amount of work/research has been already conducted for the generic VNF placement problem and VM migration for efficient resource management in CDCs, network latency among various network components and VNF migration problem have not been comprehensively considered yet to the best of our knowledge. Firstly, to address VNF placement problem, we design a more comprehensive model based on real measurements to capture network latency among VNFs with more granularity to optimize placement of VNFs in CDCs. We consider resource demand of VNFs, resource capacity of VMs and network latency among various network components. Our objectives are to minimize both network latency and lead time (the time to find a VM to host a VNF). Experimental results are promising and indicate that our approach, namely VNF Low-Latency Placement (VNF-LLP), can reduce network latency by up to 64.24% compared with two generic algorithms. Furthermore, it has a lower lead time as compared with the VNF Best-Fit Placement algorithm. Secondly, to address VNF migration problem, we i) formulate the VNF migration problem and ii) develop a novel VNF migration algorithm called VNF Real-time Migration (VNF-RM) for lower network latency in dynamically changing resource availability. As a result of experiments, the effectiveness of our algorithm is demonstrated by reducing network latency by up to 59.45% after latency-aware VNF migrations.