In this chapter we examine the capacity of a single-user wireless channel where transmitter and/or receiver have a single antenna. We will discuss capacity for channels that are both time invariant and time varying. We ﬁrst look at the well-known formula for capacity of a time-invariant additive white Gaussian noise (AWGN) channel and then consider capacity of time-varying ﬂat fading channels. We will ﬁrst consider ﬂat fading channel capacity where only the fading distribution is known at the transmitter and receiver. We will also treat capacity of frequency-selective fading channels. For time -invariant frequency-selective channels the capacity is known and is achieved with an optimal power allocation that water-ﬁlls over frequency instead of time. We will consider only discrete-time systems in this chapter.