Union membership and clout has been dropping in the US economy for decades. But it's not just a US phenomenon: a similar drop is happening in many high-income countries. The OECD Employment Outlook 2017 discussed the evidence in "Chapter 4: Collective Bargaining in a Changing World of Work."
Here are a couple of illustrative figures. Across the OECD countries, about 17% of workers belong to a union. As the report notes: "Trade union density has been declining steadily in most OECD and accession countries over the last three decades (Figure 4.2). Only Iceland, Belgium, and Spain have experienced a (very) small increase in trade union density since 1985 ..." In each of the panels, the solid black line is the overall OECD average, for ease of comparison.
Here's a parallel figure showing comparisons across countries for "collective bargaining coverage," which is the share of employees covered by collective bargaining agreements. On average, union bargaining coverage in OECD countries declined from 45% in 1985 to 33% by 2013.
The distinction between these figures should make the point that a number of countries have rules which in some cases require that firms pay non-union workers similarly to union workers. Conversely, many of the same countries also have a raft of possible exceptions to these rules. The OECD chapter provides a more detailed discussion of these ins and outs. But several overall patterns seem clear.
1) Labor union power is weaker just about everywhere.
2) The extent of labor union power varies considerably across countries, many of which have roughly similar income levels. This pattern suggests that existence of unions, one way or another, may be less important for economic outcomes than the way in which those unions function. The chapter notes the importance of "peaceful and cooperative industrial relations," which can emerge--or not--from varying patterns of unionization.
3) In the next few decades, the big-picture question for union workers, and indeed for all workers, is how to adjust their workplace skills and tasks so that they remain valued contributors in an economy characterized by new technologies and global ties. Workers need political representation--whether in the form of unions or in some other form--that goes beyond arguing for near-term pay raises, and considers the difficult problem of how to raise the chances for sustained pay raises and secure jobs into the future.