We prove both the outage theorem and its converse for block fading discrete memoryless channel. If P_out is the outage probability for the rate R then any transmission rate below R together with any average error probability greater than P_out is achievable. Conversely, for any code with rate slightly greater than R the error probability is greater than any number smaller than P_out, for large codeword lengths. Two cases are considered depending on whether the transmitter has channel state information (CSI) or not.