ShengBTE is a software package for computing the lattice thermal conductivity of crystalline bulk materials and nanowires with diffusive boundary conditions. It is based on a full iterative solution to the Boltzmann transport equation. Its main inputs are sets of second- and third-order interatomic force constants, which can be calculated using third-party ab-initio packages. Dirac delta distributions arising from conservation of energy are approximated by Gaussian functions. A locally adaptive algorithm is used to determine each process-specific broadening parameter, which renders the method fully parameter free. The code is free software, written in Fortran and parallelized using MPI. A complementary Python script to help compute third-order interatomic force constants from a minimum number of ab-initio calculations, using a real-space finite-difference approach, is also publicly available for download. Here we discuss the design and implementation of both pieces of software and present results for three example systems: Si, InAs and lonsdaleite.