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This paper investigates basic trade-offs between energy and delay in wireless communication systems using finite blocklength theory. We first assume that data arrive in constant stream of bits, which are put into packets and transmitted over a communications link. Our results show that depending on exactly how energy is measured, in general energy depends on sqrt{d^{-1}} or sqrt{d^{-1}log d}, where d is the delay. This means that the energy decreases quite slowly with increasing delay. Furthermore, to approach the absolute minimum of -1.59 dB on energy, bandwidth has to increase very rapidly, much more than what is predicted by infinite blocklength theory. We then consider the scenario when data arrive stochastically in packets and can be queued. We devise a scheduling algorithm based on finite blocklength theory and develop bounds for the energy-delay performance. Our results again show that the energy decreases quite slowly with increasing delay.