Some challenges and limitations of Parzen Windows include: 1. Computational complexity: The method requires calculating the kernel function for each data point, which can be computationally expensive for large datasets. 2. Bandwidth selection: Choosing the appropriate bandwidth is crucial for accurate density estimation, but it can be difficult to determine the optimal value. 3. Sensitivity to kernel choice: The choice of kernel function can affect the smoothness and accuracy of the density estimation, and different kernels may yield different results. 4. Curse of dimensionality: As the dimensionality of the data increases, the performance of Parzen Windows may degrade due to the increased sparsity of the data.