Manifold learning is a type of unsupervised learning technique that focuses on the nonlinear structure of data. The goal is to reduce the dimensionality of the data while preserving the relationships or structures within it. It is particularly useful when dealing with high-dimensional data where linear methods like PCA might not be appropriate.

In manifold learning, the idea is to capture the underlying manifold, or surface, on which the data resides. This underlying manifold is often of much lower dimensionality than the original space, and capturing it can help in visualizing, understanding, and analyzing the data.

Common manifold learning techniques include:

1. t-SNE (t-Distributed Stochastic Neighbor Embedding): This technique is particularly good at creating a two or three-dimensional map of the data, where similar items are close together.
2. Isomap: This method works by estimating the geodesic or ‘curved’ distance between points on the manifold.
3. Locally Linear Embedding (LLE): LLE seeks to preserve local relationships within the data and can unfold twisted manifolds.
4. Spectral Embedding: This method uses the eigenvalues of a similarity matrix to project the data into a lower-dimensional space.

Manifold learning can be applied to various domains such as image processing, speech recognition, and bioinformatics. It’s particularly useful for visualizing complex data in a way that highlights intrinsic relationships.

While manifold learning methods are powerful, they are not without their challenges. They can be sensitive to noise, tuning parameters might be tricky, and they might be computationally expensive for very large datasets.