I worked at Schlumberger full-time (More than 10 years)
I feel I should preface this review by saying that in SLB (and may be any company so large and geographically spread) there's going to be a spectrum in any category (e.g. I remember good managers I've had (2) - thru well-meaning but inept (several) - to incompetent and vindictive (1)). It also probably depends on what division/function (field, sales, technology) you've experienced. Also over the 25 years I was there the company changed (and grew) significantly. Initially the mantra was "Profits, Technology & People" - gradually I stopped seeing the "& People"; recently it seems that's now "Profits & Data Analytics").
After that preface over my 25 years with SLB by FAR the biggest "pro" is the quality of the other technical staff you can work with - some really smart people with huge experience - and the company does invest serious resources in allowing you to find technical information, share your own work and learn. This is the only reason I stayed 25 years. As with so many other aspects of the company (see Cons) YOU have to take the initiative to leverage this - formal training is more patchy, in my experience.
Compensation is good for the Oilfield Service sector - but not as good as that for the same positions in the Oil Companies themselves. The official line is they aim to be at the 50 percentile of analogous organizations and roles (per the Hayes classification system). In practice, they pay what they need to, to fill the role. You could and will be paid much more for the same job if it's located in a city where you could easily find another job with your skills (e.g. Houston), than if the competition is a (generally lower paid) university say.
If you take the initiative you can learn a lot from (the largely web-based) in-house "Professional Societies" (known internally as Eureka). It's a great resource.
Finally, the employee population is extremely diverse from a nationality/ethnic perspective. I happened to like that aspect. The company would LIKE to be more gender-diverse - that's tough in a STEM-heavy business and it's had limited success (due in part to limited effort - see Cons)
I had a friend who rose to a VP role reporting to the CEO who told me "god help this company if it ever has a competitor run by competent professional management". (It was a joke - but not entirely). I guess that reflects on SLB - and on its competitors.
My own perspective is that executive management is promoted from within (good) but with little formal training (bad) except experience from middle management roles on the way. That's compounded by at least until recently very short stays of said senior management in any one role, e.g. the current CEO resume shows, before his current job, hardly any roles which he occupied for more than two years. One person who worked for him in an earlier role told me "he put in place some procedural changes . . . it's too early to tell if they were good or bad !" (hmmm!).
Specific examples of inept executive management include (on the biggest scale) the $ 3 billion loss on the purchase and sale of SEMA back in 2003, and on a much smaller scales spending $120 million in 2007 on relocating a research facility to a different city "to encourage academic collaboration" but not increasing the collaboration budget. Both cases where failure could have been, and was predicted, but dissenting voices were ignored.
Middle Management (These are the people most employees will deal with as managers). My experience was there were a few good (effective, organized, caring of their staff, strove to get the job done despite "the system") - many well-meaning but ineffective ("box-tickers", more interested in themselves than their staff, follow the system even if it was obviously not working) - and a handful bad (self-serving, disingenuous, arbitrary).
The Culture: Chronically secretive & dis-functionally unclear lines of command, BUT a strong "we in the trenches need to get this done despite the management/system" attitude among co-workers. For example - it's almost impossible (even as a manager) to find out what the salary bands are. Not "what is Fred paid" - that's reasonable in my view, but "what's the max and min for a grade x (my grade) employee". Also there is no way (except the unofficial water-cooler) to find out what other jobs within the company are available. Trying to find out is frowned upon - A LOT. The shareholders - e.g. via yahoo finance - know more (and sooner) about the company performance than the employees (via company communication). All marked contrasts to my current employer and SLB competitor.
Decision making and chains of command are frequently confused with many stakeholders and it unclear who is making decisions. This is compounded by the perception that people have multiple managers (direct, functional, "other managers" - no-kidding there is an entry in the company directory for that). A colleague once showed me a Dilbert cartoon (with the comment "he works for Schlumberger"). It shows an inversion of the usual management pyramid, i.e. one worker reporting to 6 managers, each of whom reported to 6 managers.
A big deal is made out of the mentoring of less experience staff by older staff - that sort of makes up for the lack of career guidance by management. I NEVER in 24 years received meaningful career guidance or development through the formal chain of management. I did try to initiate the formal process once (after 24 years) and was laid-off shortly afterwards (probably a coincidence . . . probably).
Quirks - you have to propose yourself for promotion: fill out a self assessment with 5 categories (Technical Understanding - Solutions Experience - Input to Business Strategy - Mentoring & (Technical) Community Leadership - Professional Visibility); write a Proposal Letter (your manager is supposed to do it - but in my experience he will always say "draft it and I will sign it"; get letters of reference/support. The process is cumbersome (enough to discourage people in my experience) and favors "self-promoters". In practice this discourages some groups (e.g. some (but not all) women, certain cultures where "blowing your own trumpet" is regarded as distasteful). I've actually had people (women) tell me "I don't want to have to boast about myself to be recognized" and "I didn't want to embarrass you if you had to turn my request down" (I was her manager). When this failing was brought to HRs attention the (senior HR manager's) response was "tough, that's the system, they need to get over it". As I said in "Pros" the company says it would like more women - I'm skeptical that extends to changing the culture.
If you are smart, accomplished, hard-working and - critically - prepared to tell everyone about how smart, accomplished and hard-working you are, you will do well. There's a grain of truth in the criticism I've heard "Schlumberger people are so arrogant".
Advice to Management
My experience has been "Management" put limited value on my advice.
I applied through an employee referral. I interviewed at Schlumberger.
The interview process was fairly casual. I met with with 3 managers that asked basic questions about my experience and knowledge of the company. It was a friendly environment and I felt very at-ease.