This paper discusses the approaches and challenges of autoscaling in containerized applications having microservice architecture. Microservices have become a sample in development due to their flexible approach to scaling. Autoscaling allows dynamic adjustment of resources to effectively manage workload changes. Reactive autoscaling provides the ability to manage resources based on predetermined values. Proactive approach uses machine learning models to predict dynamic workloads. Hybrid method combines these methods to achieve an optimal solution. This paper evaluates the advantages and disadvantages of all approaches and suggests future research directions in autoscaling.