Graph processing has been widely used in many scenarios, from scientific computing to artificial intelligence. Graph processing exhibits irregular computational parallelism and random memory accesses, unlike traditional workloads. Therefore, running graph processing workloads on conventional architectures (e.g., CPUs and GPUs) often shows a significantly low compute-memory ratio with few performance benefits, which can be, in many cases, even slower than a specialized single-thread graph algorithm. While domain-specific hardware designs are essential for graph processing, it is still challenging to transform the hardware capability to performance boost without coupled software codesigns. This article presents a graph processing ecosystem from hardware to software. We start by introducing a series of hardware accelerators as the foundation of this ecosystem. Subsequently, the codesigned parallel graph systems and their distributed techniques are presented to support graph applications. Finally, we introduce our efforts on novel graph applications and hardware architectures. Extensive results show that various graph applications can be efficiently accelerated in this graph processing ecosystem.