This talk explores a family of recent results directed to approaching capacity at short blocklengths on the order of 50-500 channel transmissions. Convolutional codes out-perform polar codes and LDPC codes to approach the random coding union bound with low complexity when used with an optimized CRCs and list decoding. This perspective rehabilitates "catastrophic" convolutional codes, which are more properly understood for finite blocklengths as clever expurgation rather than any sort of catastrophe. This approach also provides a low-complexity approach for maximum-likelihood decoding of high-rate BCH codes. The use of variable length coding, i.e. incremental redundancy controlled with simple ACK/NACK feedback, allows capacity to be closely approached by practical codes with fewer than 500 channel uses. This talk reviews the information-theoretic results of Polyanskiy with respect to ACK/NACK feedback, presents new results extending the classic approach of Horstein for full feedback, and shows how to optimize the number and length of incremental redundancy transmissions (and feedback transmissions) for a variable-length code with feedback (i.e. a type-II hybrid ARQ). The talk also shows how to avoid entirely the overhead of a CRC in a hybrid ARQ setting by directly computing the reliability of convolutional codeword decisions. Finally, attendees will learn about a novel communications architecture that allows the use of incremental redundancy even without feedback.