A theme that continues to come up is that Mandarin does not map 1:1 to English in really subtle ways. Ways that dictionaries struggle to convey. This is why most entries in a English-Chinese dictionaries contain 5-20 possible definitions for single "words".
After about a year and a half of studying and over 2 weeks studying in China, I think I finally understand one of these multi-definitional situations I encountered.
One of the first things a student learns in a new language is to express their "wants". "I want that food", "I need water", "I want to go to the bathroom", etc. With Mandarin I immediately got into uncertain territory with something that seemed so simple. To my mind these are the verbs I need to know:
1) to want
2) to need
But in Mandarin there are a few verbs that express these concepts (I'm keeping this simple for now):
1) 要 - yao4 - to want
2) 想 - xiang3 - to want
3) 想要 - xiang3 yao4 - to want
4) 需要 - xu1 yao4 - to need
So you see the problem, there are three ways to express your "wants". So when do you use which one? Let's look at some additional layers of meaning to these words.
1) 要 - yao4 - to need, will, to ask for
Oh dear, now this overlaps with #4 as well. And wait, it indicates future tense as well, as in "I will eat this food" rather than just "I want to eat this food". And that is where the key lies, using 要 is a very aggressive "need/want". It comes with built in intent. Not only do I WANT it, but I NEED it and I WILL have it soon. Pretty powerful, right? So I use it to ask for a cup of coffee in the morning. And I get it every time!
In English we say "where there is a will there is a way". In Mandarin, 要 expresses the want and the will at the same time. If you lack the will, you probably need to use a different verb.
The first time I learned this word was in Tiananmen Square in Beijing. When approached by sellers, simply say: 不要（bu yao) and they will understand you do NOT WANT their stuff. Later I learned softer ways to say no.
2) 想 - xiang3 - to miss, to ponder, to wish
I'm starting to think of this one as the delicate flower of the "wants". It is a soft kind of wanting, it is the kind of wanting you do when you are dreaming of something that you probably won't get in the near future. You may be pondering this want, nurturing the seed of desire which may blossom into 想要 or perhaps all the way to 要, but that will be later. Right now, you simply 想.
You also use this one to tell someone you MISS them, because you are THINKING about them, and you WANT them to be near you.
Today in class we were discussing different approaches to studying Mandarin. Some students do not take their own notes and do not review the notes the teacher takes. They show up and wait for the teacher to feed them information. I responded: 他们"想"学中文，但是他们"不要"学中文。They wish (想) to learn Mandarin, but they do not really have the will (不要) to learn Mandarin.
And in that moment I understood how powerful these words were, how much is packed into such a compact space. In English we might say, "you say you want it, but do you really want it?". We use the modifier "really" to take "want" from a wish to more of a "need".
3) 想要 - xiang3 yao4 - to feel like, to desire
Now this last one I think is like a softer form of 要. There is more will than in 想, but not yet so determined as to justify 要. I'm sure with more time and exposure I will unwrap more of its subtlety.
现在我"要"睡觉。And now, I need/want/will go to sleep.