We give a survey on graphs with fixed smallest adjacency eigenvalue, especially on graphs with large minimal valency and also on graphs with good structures. Our survey mainly consists of the following two parts:

1. (i)

   Hoffman graphs, the basic theory related to Hoffman graphs and the applications of Hoffman graphs to graphs with fixed smallest adjacency eigenvalue and large minimal valency;

2. (ii)

   recent results on distance-regular graphs and co-edge regular graphs with fixed smallest adjacency eigenvalue and the characterizations of certain families of distance-regular graphs.

At the end of the survey, we also discuss signed graphs with fixed smallest adjacency eigenvalue and present some new findings.

我们对具有固定最小邻接特征值的图进行了调查，尤其是对具有最小最小化合价的图以及具有良好结构的图。我们的调查主要包括以下两个部分：

1. （一世）

   霍夫曼图，霍夫曼图的基本理论以及霍夫曼图在固定最小邻接特征值和最小化合价的图中的应用；

2. （ii）

   具有固定最小邻接特征值的距离正则图和共边正则图的最新结果以及某些距离正则图族的特征。

在调查的最后，我们还讨论了具有固定最小邻接特征值的带符号图，并提出了一些新发现。