The quantitative analysis of complex systems may be assisted by the use of methods derived from neural networks. The analysis of chaotic time series presents an applied challenge toward determining the features involved and particularly the effective complexity they include. This chapter shows that the use of chaotic autoencodersAutoencoders made of neural networks leads to essential information on the time series and the chaotic systems they arise from. The autoencoders we construct map identically the input chaotic time series to the output. The process passes through the latent space that acts as an information bottleneck for this reconstruction. We estimate the dimension of the latent space numerically and find it smaller than possible embedding dimensions of the reconstruction. The dimension of the latent space hints toward the complexity of the dynamical system underlying the time series. Furthermore, we show that the constructed chaotic autoencoders produce maximal Lyapunov exponents that are very close to those obtained directly from the equations of motion of the chaotic systems. These features show that the constructed chaotic autoencoders are faithful representations of the time series generating dynamical systems, and through their latent space dimension, we obtain an estimate of their complexity.