The threshold theorem for fault tolerance tells us that it is possible to build arbitrarily large reliable quantum computers provided the error rate per physical gate or time step is below some threshold value. The leading candidate for realizing fault tolerance is the surface code, which admits a 2-dimensional layout, has a high error threshold, and has large but not ridiculous overhead (in terms of extra qubits needed). I will discuss another approach which has garnered interest in recent years since it has the potential to greatly decrease the overhead: namely, using high-rate low-density parity check codes, known as LDPC codes. We do not yet have practical protocols using LDPC codes, so I will explain the progress so far in finding interesting codes, decoding algorithms for them, and fault-tolerant operations on them.