Pros
Decent salary and good benefits. People are generally nice. Can be really cushy if you're OK just doing the minimum to get a good review/bonus. I think the happiest people are the ones who find a sweet spot and ride things out for a long period (long-term benefits are great).
Cons
We're in a slowly dying industry and lack a clear direction forward. This is reflected in our inability to attract and retain talent from top universities. Think to yourself, why would an engineer from Stanford go to Chevron instead of a tech firm? Internally, we have an exhausting bureaucracy that is highly political and difficult to navigate. At the heart, this is an engineering company, and it is presumed that engineers can do anything. In an era of changing dynamics and enormous pressure from investors and policymakers to move away from fossil fuels, the old school engineer mentality could end up being our downfall. If you're not an engineer (i.e., you're a market analyst, economist, climate person) I'd recommend staying away--you're career path will likely be limited here, and you'll be frustrated by the slow pace, extra work to deal with enormous overhead, and lack of clarity on our goals.