Monitoring the evolutionary responses of species to ongoing global climate change is critical for informing conservation. Population genomic studies that use samples from multiple time points ("temporal genomics") are uniquely able to make direct observations of change over time. Consequently, only temporal studies can show genetic erosion or spatiotemporal changes in population structure. Temporal genomic studies directly examining climate change effects are currently rare but will likely increase in the coming years due to their high conservation value. Here, we highlight four key genetic indicators that can be monitored using temporal genomics to understand how species are responding to climate change. All indicators crucially rely on having a suitable baseline that accurately represents the past condition of the population, and we discuss aspects of study design that must be considered to achieve this.