If your company doesn't do reviews formally, don't ask for a formal review. Instead have a conversation with your boss in a private meeting where you ask him specifically what you can do to get to the next level and present your case, based on your achievements (many of which he may not actually be aware of), if you might want a raise. Ask him if there are any places where you need to improve. No need to be formal, it is your boss's job to discuss your performance with you whether they do a formal review or not.
Personally I talk to my boss all the time about performance and priorities, etc, so there is no surprises for me when formal reviews come around. Remember performance rewards are dependent on what people perceive about your performance not necessarily what you think about it. You can't focus on what you need until you know how you are perceived. If things start to take a negative turn (which happens eventually to everyone) it is far better for your reputation to be perceived as noticing and fixing it before it gets worse than to tootle along happily until an annual review when you get socked with a problem you didn't even know you had. In fact when you are having an issue or going to miss a deadline, etc. talking to your boss immediately is usually the best thing you can do because I assure you that he is going to be even more unhappy to hear about it after it is no longer fixable or to hear bad news about you from someone else.
If you talk informally about performance regularly, you can make sure to never have a bad appraisal. If there is a problem, the formal review is too late to address it. Informal discussions mean you have a chance to address problems before a review or before they choose to let you go. If you want a reward, it is often best to get it while a large achievement is fresh in everyone's mind. If you want a promotion, then you ask what specific things you need to do to show you are ready and you ask to be assigned to the tasks that will get you that experience. I remember being quite surprised when I was young that what my boss thought I needed to have to be promoted did not agree at all with what I thought I needed.