Smale's h-cobordism theorem has been one of the most influential results in topology, so much that the conventional line of separation between "low" and "high" dimensions is drawn between dimensions 4 and 5 because the h-cobordism holds true in dimension greater or equal to 5. During the talk I will try to give the key idea of the h-cobordism theorem (the so-called Whitney trick), and why it holds only in high dimensions. Time permitting, I will discuss some related problems, such as the generalised Poincaré conjecture.