In this tutorial particular attention is given to the computing power in the physical layer of wireless devices, which are energy and power limited. Communication uses the power in the analog radio frequency parts and computation uses power in the signal processing and other tasks required during communication, both in the transmitter and in the receiver. Example applications include sensor networks and mobile devices in ultra-dense small cell networks where the link distances are below about 10 m, and the computing power is larger than the communication power. The computation-communication tradeoff means that if one of the powers is increased, the other one must be decreased, otherwise the total power increases. Energy efficiency is a challenging multidisciplinary topic, and the consequences of the interrelated fundamental limits are not well understood. According to Edholm's prediction, the link bit rates are increasing exponentially each year, which implies that there must be a corresponding exponential trend in improving energy efficiency, defined as number of bits per energy unit, both in computation and communication. It is well known that for communications, due to noise, the Shannon limit forms the fundamental limit for the received energy per bit, but in computation there is a similar limit called Landauer limit for the switching energy of a transistor. Near the two fundamental limits the energy efficiency cannot be improved any more exponentially. Our main contribution is to elaborate the connections between the various technology predictions, different fundamental limits and possible design trade-offs. Specifically, we show that because of the aforementioned fundamental limits, the exponential trends in bit rates cannot continue without a compensating exponential trend in energy efficiency. We also revisit the concept of crossover distance and derive it from the fundamental limits to give some further system-level insight on the energy consumption bottlenecks.