CUDA has a complex memory model that involves different types and scopes of memory, each with their own characteristics and trade-offs. Local memory is the private memory of each thread, allocated on the global memory with high latency and low bandwidth, and should be avoided if possible. Shared memory is fast and low-latency, shared by all threads within a block for data exchange and synchronization, and should be used for frequently accessed or reused data. Global memory is large and persistent, accessible by all threads across the grid, and should store input and output data. Constant memory is read-only and cached, accessible by all threads across the grid, and should store data that is constant or uniform for all threads. Lastly, texture memory is read-only and cached, optimized for 2D spatial locality, and should store data accessed with 2D patterns such as images or matrices. These types of memory must be optimized for usage by minimizing transfers, coalescing accesses, using memory fences and atomic operations, avoiding bank conflicts, aligning and padding data structures, using linear filtering and addressing modes.