A key practical constraint on the design of Hybrid automatic repeat request (HARQ) schemes is the modem chip area that needs to be allocated to store previously received packets. The fact that, in modern wireless standards, this area can amount to a large fraction of the overall chip has recently highlighted the importance of HARQ buffer management, that is, of the use of advanced compression policies for storage of received data. This work tackles the analysis of the throughput of standard HARQ schemes, namely Type-I, Chase Combining and Incremental Redundancy, under the assumption of a finite-capacity HARQ buffer by taking an information-theoretic standpoint based on random coding. Both coded modulation, via Gaussian signaling, and Bit Interleaved Coded Modulation (BICM) are considered. The analysis sheds light on questions of practical relevance for HARQ buffer management such as on the type of information to be extracted from the received packets and on how to store it.